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3https://getlykke-assets.s3.amazonaws.com/wiki-posters/c1db9d13-7c92-4fd1-907a-12c411711f47_score-analysis.jpegCase Studies: Score Analysis image 1Case Studies: Score Analysis - Music Appreciation 1 - image 1https://www.getlykke.com/explore/public/music-appreciation-1-3382b0df-6758-42c8-b2ad-c3f8655391d1/media/score-analysis/svg/1Case Studies: Score Analysis diagram 1Case Studies: Score Analysis - Music Appreciation 1 - diagram 1https://www.getlykke.com/explore/public/music-appreciation-1-3382b0df-6758-42c8-b2ad-c3f8655391d1/media/score-analysis/svg/2Case Studies: Score Analysis diagram 2Case Studies: Score Analysis - Music Appreciation 1 - diagram 2https://www.getlykke.com/explore/public/music-appreciation-1-3382b0df-6758-42c8-b2ad-c3f8655391d1/media/score-analysis/svg/3Case Studies: Score Analysis diagram 3Case Studies: Score Analysis - Music Appreciation 1 - diagram 3https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b2026-04-20T05:11:21.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1px">THE OER ECOSYSTEM</text> <text x="450" y="78" text-anchor="middle" font-family="system-ui, sans-serif" font-size="15" fill="#94a3b8" font-weight="400">Transforming Static Content into Dynamic Learning Architecture</text> <line x1="350" y1="95" x2="550" y2="95" stroke="#38bdf8" stroke-width="2" stroke-linecap="round"/> <!-- Left Panel: The 5 Rs Framework --> <rect x="40" y="120" width="400" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="150" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#f59e0b">THE 5 Rs FRAMEWORK</text> <text x="60" y="170" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8">The legal pillars of Open Educational Resources</text> <!-- R1: Retain --> <g transform="translate(60, 195)"> <circle r="15" cx="15" cy="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <path d="M10 15h10M15 10v10" stroke="#f59e0b" stroke-width="2" stroke-linecap="round" transform="rotate(45 15 15)"/> <text x="45" y="14" font-family="system-ui, sans-serif" font-weight="700" font-size="14" fill="#f8fafc">RETAIN</text> <text x="45" y="28" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">The right to make, own, and control copies.</text> </g> <!-- R2: Reuse --> <g transform="translate(60, 250)"> <circle r="15" cx="15" cy="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <path d="M10 15a5 5 0 1 1 5 5m0-10l3 3-3 3" fill="none" stroke="#f59e0b" stroke-width="2" stroke-linecap="round"/> <text x="45" y="14" font-family="system-ui, sans-serif" font-weight="700" font-size="14" fill="#f8fafc">REUSE</text> <text x="45" y="28" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">The right to use content in diverse ways.</text> </g> <!-- R3: Revise --> <g transform="translate(60, 305)"> <circle r="15" cx="15" cy="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <path d="M10 20l10-10 2 2-10 10-2-2z" fill="none" stroke="#f59e0b" stroke-width="1.5"/> <text x="45" y="14" font-family="system-ui, sans-serif" font-weight="700" font-size="14" fill="#f8fafc">REVISE</text> <text x="45" y="28" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">The right to adapt, adjust, or modify.</text> </g> <!-- R4: Remix --> <g transform="translate(60, 360)"> <circle r="15" cx="15" cy="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <circle cx="12" cy="15" r="5" fill="none" stroke="#f59e0b" stroke-width="1.5"/> <circle cx="18" cy="15" r="5" fill="none" stroke="#f59e0b" stroke-width="1.5"/> <text x="45" y="14" font-family="system-ui, sans-serif" font-weight="700" font-size="14" fill="#f8fafc">REMIX</text> <text x="45" y="28" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">The right to combine with other materials.</text> </g> <!-- R5: Redistribute --> <g transform="translate(60, 415)"> <circle r="15" cx="15" cy="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <circle cx="15" cy="12" r="2" fill="#f59e0b"/> <circle cx="11" cy="18" r="2" fill="#f59e0b"/> <circle cx="19" cy="18" r="2" fill="#f59e0b"/> <path d="M15 12l-4 6M15 12l4 6" stroke="#f59e0b" stroke-width="1.5"/> <text x="45" y="14" font-family="system-ui, sans-serif" font-weight="700" font-size="14" fill="#f8fafc">REDISTRIBUTE</text> <text x="45" y="28" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">The right to share copies with others.</text> </g> <!-- Right Top Panel: Digital Courseware Stack --> <rect x="460" y="120" width="400" height="210" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="480" y="150" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#38bdf8">MODERN TECH STACK</text> <!-- Stack Layers --> <g transform="translate(480, 170)"> <!-- Layer 3 --> <rect x="0" y="100" width="360" height="30" rx="4" fill="#38bdf820" stroke="#38bdf8"/> <text x="180" y="120" text-anchor="middle" font-family="system-ui, sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">LMS INTEGRATION (LTI)</text> <!-- Layer 2 --> <rect x="20" y="65" width="320" height="30" rx="4" fill="#38bdf840" stroke="#38bdf8"/> <text x="180" y="85" text-anchor="middle" font-family="system-ui, sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">ASSESSMENT ENGINES</text> <!-- Layer 1 --> <rect x="40" y="30" width="280" height="30" rx="4" fill="#38bdf8" stroke="#38bdf8"/> <text x="180" y="50" text-anchor="middle" font-family="system-ui, sans-serif" font-size="12" font-weight="bold" fill="#0f172a">ANALYTICS LAYER</text> <path d="M180 25V10" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2"/> <text x="180" y="5" text-anchor="middle" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8" font-style="italic">Continuous Improvement Loop</text> </g> <!-- Right Bottom Panel: Creative Commons --> <rect x="460" y="345" width="400" height="175" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="480" y="375" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#e879f9">LICENSING (CC)</text> <g transform="translate(480, 395)"> <!-- BY --> <circle cx="30" cy="30" r="25" fill="#e879f915" stroke="#e879f9" stroke-width="1.5"/> <text x="30" y="36" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="bold" font-size="16" fill="#e879f9">BY</text> <text x="30" y="70" text-anchor="middle" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">Attribution</text> <!-- SA --> <circle cx="110" cy="30" r="25" fill="#e879f915" stroke="#e879f9" stroke-width="1.5"/> <text x="110" y="36" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="bold" font-size="16" fill="#e879f9">SA</text> <text x="110" y="70" text-anchor="middle" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">ShareAlike</text> <!-- NC --> <circle cx="190" cy="30" r="25" fill="#e879f915" stroke="#e879f9" stroke-width="1.5"/> <text x="190" y="36" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="bold" font-size="16" fill="#e879f9">NC</text> <text x="190" y="70" text-anchor="middle" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">Non-Comm.</text> <!-- ND --> <circle cx="270" cy="30" r="25" fill="#ffffff10" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="3 2"/> <text x="270" y="36" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="bold" font-size="16" fill="#94a3b8">ND</text> <text x="270" y="70" text-anchor="middle" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">Non-Deriv.</text> <text x="0" y="100" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8" font-style="italic">Note: ND (No Derivatives) is not considered true OER.</text> </g> <!-- Footer --> <text x="860" y="540" text-anchor="end" font-family="system-ui, sans-serif" font-size="10" fill="#ffffff30">LUMEN LEARNING // COURSE INTRODUCTION</text> </svg>Course Introduction and Open Educational Resources image 1Course Introduction and Open Educational Resources - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/course-introduction-oer/svg/1Course Introduction and Open Educational Resources diagram 1Course Introduction and Open Educational Resources - Introduction to Literature - diagram 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/course-introduction-oer/svg/2Course Introduction and Open Educational Resources diagram 2Course Introduction and Open Educational Resources - Introduction to Literature - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Background and Textures --> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> </defs> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="450" y="55" text-anchor="middle" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">DEFINING LITERATURE &amp; ACADEMIC STANDARDS</text> <rect x="350" y="70" width="200" height="4" fill="url(#accentGrad)" rx="2"/> <text x="450" y="95" text-anchor="middle" font-family="Arial, sans-serif" font-size="14" fill="#94a3b8" font-style="italic">From "Great Books" to Dynamic Systems of Human Expression</text> <!-- Left Column: The Evolution Timeline --> <rect x="30" y="130" width="260" height="390" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="50" y="160" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">I. EVOLUTION OF SCOPE</text> <!-- Timeline Path --> <path d="M 60 190 L 60 480" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 4" opacity="0.4"/> <!-- Era 1 --> <circle cx="60" cy="200" r="6" fill="#38bdf8"/> <text x="75" y="200" font-family="Arial, sans-serif" font-weight="bold" font-size="13" fill="#f8fafc">CLASSICAL / MEDIEVAL</text> <text x="75" y="218" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Litteratura: General learning &amp; grammar.</text> <!-- Era 2 --> <circle cx="60" cy="270" r="6" fill="#38bdf8"/> <text x="75" y="270" font-family="Arial, sans-serif" font-weight="bold" font-size="13" fill="#f8fafc">RENAISSANCE</text> <text x="75" y="288" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Belles-lettres: Rhetoric and style.</text> <!-- Era 3 --> <circle cx="60" cy="340" r="6" fill="#38bdf8"/> <text x="75" y="340" font-family="Arial, sans-serif" font-weight="bold" font-size="13" fill="#f8fafc">ROMANTIC / VICTORIAN</text> <text x="75" y="358" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Imaginative Art: The "Genius" author.</text> <!-- Era 4 --> <circle cx="60" cy="410" r="6" fill="#38bdf8"/> <text x="75" y="410" font-family="Arial, sans-serif" font-weight="bold" font-size="13" fill="#f8fafc">POST-MODERN</text> <text x="75" y="428" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Textuality: Inclusive of all cultural artifacts.</text> <!-- Center Column: The Mechanics of Merit --> <rect x="310" y="130" width="280" height="220" rx="16" fill="#ffffff12" stroke="#f59e0b" stroke-width="1" stroke-opacity="0.3"/> <text x="330" y="160" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">II. THE CANON FORMULA</text> <!-- Formula Box --> <rect x="330" y="180" width="240" height="60" rx="8" fill="#00000044"/> <text x="450" y="218" text-anchor="middle" font-family="Georgia, serif" font-size="22" fill="#f8fafc">C(t) = ∫ (A·S + I·R) dt</text> <!-- Variables --> <g font-family="Arial, sans-serif" font-size="11" fill="#94a3b8"> <text x="335" y="265"><tspan fill="#f59e0b" font-weight="bold">A</tspan> Aesthetic Innovation</text> <text x="335" y="285"><tspan fill="#f59e0b" font-weight="bold">S</tspan> Semantic Density</text> <text x="465" y="265"><tspan fill="#f59e0b" font-weight="bold">I</tspan> Intertextual Influence</text> <text x="465" y="285"><tspan fill="#f59e0b" font-weight="bold">R</tspan> Cultural Resonance</text> </g> <text x="330" y="320" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc" font-style="italic" opacity="0.8">"Canonicity is a function of formal uniqueness</text> <text x="330" y="335" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc" font-style="italic" opacity="0.8">multiplied by its impact over time."</text> <!-- Bottom Center: Oral Tradition --> <rect x="310" y="370" width="280" height="150" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="330" y="400" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">III. 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fill="#ffffff12" stroke="#ffffff25" stroke-width="1"/> <circle cx="500" cy="180" r="20" fill="#f59e0b20"/> <rect x="492" y="172" width="16" height="16" stroke="#f59e0b" stroke-width="2" fill="none"/> <text x="530" y="185" font-family="sans-serif" font-size="18" font-weight="700" fill="#f59e0b">The Architect</text> <text x="490" y="230" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">GOAL: Technique Identification</text> <text x="490" y="250" font-family="sans-serif" font-size="12" fill="#94a3b8">Focuses on syntax, diction, and structural choices.</text> <text x="490" y="290" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">TEMPORAL VIEW: Recursive</text> <text x="490" y="310" font-family="sans-serif" font-size="12" fill="#94a3b8">Back-and-forth analysis of linguistic patterns.</text> <path d="M490 350 L790 350" stroke="#ffffff20" stroke-width="1" stroke-dasharray="4 4"/> <text x="490" y="380" font-family="sans-serif" font-size="13" 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force."</text> <text x="450" y="520" font-family="sans-serif" font-weight="700" font-size="11" fill="#38bdf8" text-anchor="middle" letter-spacing="2">— THE LAW OF NARRATIVE INERTIA</text> <!-- Arrowhead definition --> <defs> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="#f8fafc" /> </marker> </defs> </svg>Narrative Elements: Conflict and Plot image 1Narrative Elements: Conflict and Plot - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/narrative-elements-conflict-and-plot/svg/1Narrative Elements: Conflict and Plot diagram 1Narrative Elements: Conflict and Plot - Introduction to Literature - diagram 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/narrative-elements-conflict-and-plot/svg/2Narrative Elements: Conflict and Plot diagram 2Narrative Elements: Conflict and Plot - Introduction to Literature - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background Layer --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">LITERARY ELEMENTS: THE SEMANTIC LAYER</text> <path d="M 300 65 L 600 65" stroke="url(#accentGrad)" stroke-width="3" stroke-linecap="round"/> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="2">THE ARCHITECTURE OF THEME &amp; SYMBOLISM</text> <!-- Left Column: THEME --> <rect x="40" y="110" width="400" height="410" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="80" cy="145" r="18" fill="#f59e0b22" stroke="#f59e0b" stroke-width="2"/> <path d="M 74 145 L 86 145 M 80 139 L 80 151" stroke="#f59e0b" stroke-width="2"/> <text x="110" y="152" font-family="sans-serif" font-weight="700" font-size="22" fill="#f59e0b">THEME</text> <text x="110" y="170" font-family="sans-serif" font-size="12" fill="#94a3b8">The "Objective Function" of Narrative</text> <!-- Theme Content: Concept vs Statement --> <rect x="60" y="195" width="360" height="85" rx="8" fill="#00000033"/> <text x="75" 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It ensures</tspan> <tspan x="75" dy="18">every plot module serves a unified purpose.</tspan> </text> <!-- Right Column: SYMBOLISM --> <rect x="460" y="110" width="400" height="410" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="500" cy="145" r="18" fill="#38bdf822" stroke="#38bdf8" stroke-width="2"/> <path d="M 495 150 L 505 140 M 505 140 L 500 140 M 505 140 L 505 145" stroke="#38bdf8" stroke-width="2" fill="none"/> <text x="530" y="152" font-family="sans-serif" font-weight="700" font-size="22" fill="#38bdf8">SYMBOLISM</text> <text x="530" y="170" font-family="sans-serif" font-size="12" fill="#94a3b8">The Pointer System of Literature</text> <!-- Symbolism Mapping Function --> <rect x="480" y="195" width="360" height="85" rx="8" fill="#00000033"/> <text x="495" y="215" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Mapping Function: f: L → A</text> <circle cx="530" cy="245" r="15" fill="#38bdf844" stroke="#38bdf8"/> <text x="530" y="249" text-anchor="middle" font-family="serif" font-size="12" fill="#f8fafc">L</text> <text x="530" y="272" text-anchor="middle" font-family="sans-serif" font-size="9" fill="#94a3b8">LITERAL</text> <path d="M 555 245 L 615 245" stroke="#f8fafc" stroke-width="2" marker-end="url(#arrowhead)"/> <text x="585" y="235" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#e879f9">POINTER</text> <rect x="625" y="230" width="30" height="30" fill="#e879f944" stroke="#e879f9" transform="rotate(45, 640, 245)"/> <text x="640" y="249" text-anchor="middle" font-family="serif" font-size="12" fill="#f8fafc">A</text> <text x="640" y="272" text-anchor="middle" font-family="sans-serif" font-size="9" fill="#94a3b8">ABSTRACT</text> <!-- Symbol Categories --> <g transform="translate(480, 300)"> <text x="15" y="15" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Symbol Categories</text> <rect y="30" width="170" height="60" rx="8" fill="#ffffff08"/> <text x="10" y="50" font-family="sans-serif" font-weight="600" font-size="12" fill="#38bdf8">Conventional</text> <text x="10" y="70" font-family="sans-serif" font-size="10" fill="#94a3b8">Universal recognition</text> <text x="10" y="82" font-family="sans-serif" font-size="10" fill="#94a3b8">Ex: Skull = Death</text> <rect x="180" y="30" width="170" height="60" rx="8" fill="#ffffff08"/> <text x="190" y="50" font-family="sans-serif" font-weight="600" font-size="12" fill="#e879f9">Contextual</text> <text x="190" y="70" font-family="sans-serif" font-size="10" fill="#94a3b8">Internal "runtime" only</text> <text x="190" y="82" font-family="sans-serif" font-size="10" fill="#94a3b8">Ex: Gatsby's Green Light</text> </g> <text x="495" y="425" font-family="sans-serif" font-size="12" fill="#94a3b8"> <tspan x="495" dy="0">Symbols are variables that reference memory</tspan> <tspan x="495" dy="18">addresses within the collective human condition.</tspan> </text> <!-- Central Connection --> <path d="M 440 315 L 460 315" stroke="url(#accentGrad)" stroke-width="2" stroke-dasharray="4,2"/> <circle cx="450" cy="315" r="4" fill="#f8fafc"/> <!-- Footer --> <rect x="40" y="530" width="820" height="1" fill="#ffffff22"/> <text x="40" y="550" font-family="sans-serif" font-size="10" fill="#64748b">WIKI SECTION: LITERARY ANALYSIS 101</text> <text x="860" y="550" text-anchor="end" font-family="sans-serif" font-size="10" fill="#64748b">FORMALISM &amp; SEMANTICS</text> <!-- Arrowhead marker --> <defs> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="#f8fafc" /> </marker> </defs> </svg>Literary Elements: Theme and Symbolism image 1Literary Elements: Theme and Symbolism - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/literary-elements-theme-and-symbolism/svg/1Literary Elements: Theme and Symbolism diagram 1Literary Elements: Theme and 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y="400" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Iceberg Theory</text> <text x="665" y="415" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Stream of Consciousness</text> <text x="665" y="430" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Minimalist Syntax</text> <!-- Mechanics of Style Panel --> <rect x="40" y="475" width="820" height="65" rx="8" fill="#00000040" stroke="#ffffff15"/> <text x="60" y="495" font-family="sans-serif" font-weight="bold" font-size="12" fill="#38bdf8" text-transform="uppercase">The Mechanics of Style</text> <text x="60" y="518" font-family="sans-serif" font-size="11" fill="#94a3b8">DICTION:</text> <text x="120" y="518" font-family="sans-serif" font-size="11" fill="#f8fafc">Latinate/Polysyllabic vs. Germanic/Monosyllabic</text> <text x="420" y="518" font-family="sans-serif" font-size="11" fill="#94a3b8">SYNTAX:</text> <text x="480" y="518" font-family="sans-serif" font-size="11" fill="#f8fafc">Hypotactic (Complex) vs. Paratactic (Simple)</text> <text x="60" y="533" font-family="sans-serif" font-size="11" fill="#94a3b8">STRUCTURE:</text> <text x="135" y="533" font-family="sans-serif" font-size="11" fill="#f8fafc">Periodic (End-weighted) vs. Loose (Cumulative)</text> <!-- Decorative Icons --> <!-- Quill --> <path d="M 210 145 L 220 155 M 215 150 Q 225 140 230 145" stroke="#f59e0b" stroke-width="1.5" fill="none" opacity="0.6"/> <!-- Scale --> <path d="M 400 335 L 420 335 M 410 335 L 410 350" stroke="#e879f9" stroke-width="1.5" fill="none" opacity="0.6"/> <!-- Mountain --> <path d="M 600 145 L 610 135 L 620 145" stroke="#38bdf8" stroke-width="1.5" fill="none" opacity="0.6"/> <!-- Iceberg --> <path d="M 800 350 L 810 335 L 820 350 Z" fill="#fb7185" opacity="0.3"/> <line x1="795" y1="345" x2="825" y2="345" stroke="#f8fafc" stroke-width="1" opacity="0.5"/> </svg>Literary Style and Historical Context image 1Literary Style and Historical Context - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/literary-style-and-historical-context/svg/1Literary Style and Historical Context diagram 1Literary Style and Historical Context - Introduction to Literature - diagram 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/literary-style-and-historical-context/svg/2Literary Style and Historical Context diagram 2Literary Style and Historical Context - Introduction to Literature - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg-grad" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" 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fill="#f8fafc" opacity="0.8"> <tspan x="170" dy="0">Extended metaphor where</tspan> <tspan x="170" dy="16">characters represent abstract</tspan> <tspan x="170" dy="16">moral or political ideas.</tspan> </text> <!-- Card 2: Foreshadowing --> <rect x="320" y="120" width="260" height="340" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="450" cy="160" r="25" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2"/> <path d="M 440 160 Q 450 140 460 160 T 450 180" fill="none" stroke="#f59e0b" stroke-width="2"/> <text x="450" y="210" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">FORESHADOWING</text> <text x="450" y="230" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#94a3b8">Narrative Causality</text> <!-- Foreshadowing Visual --> <line x1="360" y1="300" x2="540" y2="300" stroke="#94a3b8" stroke-width="1"/> <circle cx="380" cy="300" r="6" fill="#f59e0b"/> <text x="380" y="325" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f59e0b" font-weight="bold">THE SEED</text> <path d="M 520 300 L 535 285 M 520 300 L 535 315" stroke="#f59e0b" stroke-width="3"/> <text x="520" y="325" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f59e0b" font-weight="bold">THE PAYOFF</text> <text x="450" y="360" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#f8fafc" opacity="0.8"> <tspan x="450" dy="0">"Chekhov's Gun" logic:</tspan> <tspan x="450" dy="16">Indicative fragments that</tspan> <tspan x="450" dy="16">ensure narrative inevitability.</tspan> </text> <rect x="360" y="400" width="180" height="30" rx="8" fill="#f59e0b10" stroke="#f59e0b30"/> <text x="450" y="420" text-anchor="middle" font-family="sans-serif" font-size="10" font-style="italic" fill="#f59e0b">Temporal Logic &amp; Omens</text> <!-- Card 3: Irony --> <rect x="600" y="120" width="260" height="340" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="730" cy="160" r="25" 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id="fictionGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#e879f9" stop-opacity="0.2"/> <stop offset="100%" stop-color="#e879f9" stop-opacity="0.05"/> </linearGradient> <linearGradient id="cnfGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#38bdf8" stop-opacity="0.2"/> <stop offset="100%" stop-color="#38bdf8" stop-opacity="0.05"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#94a3b8" fill-opacity="0.1"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">GENRES: FICTION &amp; CREATIVE NONFICTION</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">The Authorial Contract and the Mechanics of the Truth Claim</text> <!-- Fiction Panel --> <rect x="40" y="110" width="390" height="300" rx="16" fill="url(#fictionGrad)" stroke="#e879f9" stroke-opacity="0.3" stroke-width="1"/> <circle cx="80" cy="150" r="20" fill="#e879f9" fill-opacity="0.2"/> <path d="M72 150 L88 150 M80 142 L80 158" stroke="#e879f9" stroke-width="2" transform="rotate(45 80 150)"/> <text x="110" y="155" font-family="sans-serif" font-weight="700" font-size="22" fill="#f8fafc">FICTION</text> <text x="65" y="195" font-family="sans-serif" font-weight="600" font-size="14" fill="#e879f9">The Fictional Pact</text> <text x="65" y="215" font-family="sans-serif" font-size="12" fill="#cbd5e1" width="340"> <tspan x="65" dy="0">Implicitly "untrue" or "imagined." The reader engages</tspan> <tspan x="65" dy="18">in the </tspan> <tspan fill="#f59e0b" font-weight="bold">Willing Suspension of Disbelief</tspan> <tspan>.</tspan> </text> <rect x="65" y="255" width="340" height="1" fill="#ffffff15"/> <text x="65" y="285" font-family="sans-serif" font-size="12" fill="#94a3b8" font-weight="bold">SOURCE MATERIAL</text> <text x="65" y="302" font-family="sans-serif" font-size="13" fill="#f8fafc">Imagination, Archetypes, Synthesis</text> <text x="65" y="340" font-family="sans-serif" font-size="12" fill="#94a3b8" font-weight="bold">ETHICAL CONSTRAINT</text> <text x="65" y="357" font-family="sans-serif" font-size="13" fill="#f8fafc">Internal Consistency &amp; Aesthetic Unity</text> <!-- CNF Panel --> <rect x="470" y="110" width="390" height="300" rx="16" fill="url(#cnfGrad)" stroke="#38bdf8" stroke-opacity="0.3" stroke-width="1"/> <circle cx="510" cy="150" r="20" fill="#38bdf8" fill-opacity="0.2"/> <circle cx="510" cy="150" r="8" stroke="#38bdf8" stroke-width="2" fill="none"/> <line x1="516" y1="156" x2="522" y2="162" stroke="#38bdf8" stroke-width="2"/> <text x="540" y="155" font-family="sans-serif" font-weight="700" font-size="22" fill="#f8fafc">CREATIVE NONFICTION</text> <text x="495" y="195" font-family="sans-serif" font-weight="600" font-size="14" fill="#38bdf8">The Referential Pact</text> <text x="495" y="215" font-family="sans-serif" font-size="12" fill="#cbd5e1"> <tspan x="495" dy="0">Explicitly "factually grounded." The reader grants</tspan> <tspan x="495" dy="18">the author </tspan> <tspan fill="#f59e0b" font-weight="bold">Epistemic Trust</tspan> <tspan> in shared reality.</tspan> </text> <rect x="495" y="255" width="340" height="1" fill="#ffffff15"/> <text x="495" y="285" font-family="sans-serif" font-size="12" fill="#94a3b8" font-weight="bold">SOURCE MATERIAL</text> <text x="495" y="302" font-family="sans-serif" font-size="13" fill="#f8fafc">Memory, Research, Records, Interviews</text> <text x="495" y="340" font-family="sans-serif" font-size="12" fill="#94a3b8" font-weight="bold">ETHICAL CONSTRAINT</text> <text x="495" y="357" font-family="sans-serif" font-size="13" fill="#f8fafc">Obligation to represent "What Happened"</text> <!-- Shared Toolkit Bridge --> <rect x="250" y="425" width="400" height="45" rx="22.5" fill="#ffffff10" stroke="#f59e0b" stroke-opacity="0.4"/> <text x="450" y="442" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f59e0b" font-weight="bold" letter-spacing="2">THE SHARED NARRATIVE TOOLKIT</text> <text x="450" y="460" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#f8fafc">Plot &amp; Arc • Characterization • Point of View • Setting • Imagery</text> <!-- Bottom Section: Formula --> <rect x="40" y="485" width="820" height="60" rx="12" fill="#00000030"/> <text x="65" y="520" font-family="serif" font-size="20" fill="#f8fafc" font-style="italic">R(T) = Σ V(eᵢ) / n</text> <text x="210" y="512" font-family="sans-serif" font-size="11" fill="#94a3b8">REFERENTIALITY INDEX:</text> <text x="210" y="528" font-family="sans-serif" font-size="12" fill="#cbd5e1">The verifiability of narrative events (e) against external records.</text> <path d="M700 510 L730 510" stroke="#e879f9" stroke-width="3" stroke-linecap="round"/> <text x="740" y="515" font-family="sans-serif" font-size="11" fill="#cbd5e1">Fiction: Claim R ≈ 0</text> <path d="M700 530 L730 530" stroke="#38bdf8" stroke-width="3" stroke-linecap="round"/> <text x="740" y="535" font-family="sans-serif" font-size="11" fill="#cbd5e1">CNF: Claim R → 1</text> <!-- Decorative Connectors --> <path d="M430 260 Q450 260 470 260" stroke="#f59e0b" stroke-width="1" stroke-dasharray="4 4" fill="none" opacity="0.5"/> <circle cx="450" cy="260" r="3" fill="#f59e0b"/> </svg>Genres: Fiction and Creative Nonfiction image 1Genres: Fiction and Creative Nonfiction - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/fiction-and-creative-nonfiction/svg/1Genres: Fiction and Creative Nonfiction diagram 1Genres: Fiction and Creative Nonfiction - Introduction to Literature - diagram 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/fiction-and-creative-nonfiction/svg/2Genres: Fiction and Creative Nonfiction diagram 2Genres: Fiction and Creative Nonfiction - Introduction to Literature - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#f59e0b"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Decorative Header Elements --> <path d="M50 60 L850 60" stroke="#ffffff20" stroke-width="1"/> <circle cx="50" cy="60" r="4" fill="#38bdf8"/> <circle cx="850" cy="60" r="4" fill="#e879f9"/> <!-- Title Section --> <text x="450" y="45" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" text-anchor="middle" letter-spacing="1">POETRY: THE LINGUISTIC MACHINE</text> <text x="450" y="78" font-family="sans-serif" font-size="14" fill="#94a3b8" text-anchor="middle" font-style="italic">Reverse-engineering the highest density of information per unit of language.</text> <!-- LEFT COLUMN: THE COLLINS FRAMEWORK --> <text x="60" y="125" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">I. THE COLLINS FRAMEWORK</text> <text x="60" y="145" font-family="sans-serif" font-size="12" fill="#94a3b8">Modes of engagement to "activate" the poetic contract.</text> <!-- Mode 1: Color Probe --> <rect x="60" y="165" width="360" height="65" rx="12" fill="#ffffff10"/> <rect x="75" y="178" width="40" height="40" rx="6" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <path d="M85 188 L105 208 M105 188 L85 208" stroke="#f59e0b" stroke-width="2" opacity="0.8"/> <text x="130" y="188" font-family="sans-serif" font-weight="700" font-size="15" fill="#f8fafc">Color Probe</text> <text x="130" y="205" font-family="sans-serif" font-size="12" fill="#94a3b8">Holding the poem to light to find tonal shifts.</text> <!-- Mode 2: Acoustic Testing --> <rect x="60" y="240" width="360" height="65" rx="12" fill="#ffffff10"/> <rect x="75" y="253" width="40" height="40" rx="6" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <circle cx="95" cy="273" r="8" stroke="#38bdf8" fill="none" stroke-width="1.5"/> <circle cx="95" cy="273" r="4" fill="#38bdf8"/> <text x="130" y="263" font-family="sans-serif" font-weight="700" font-size="15" fill="#f8fafc">Acoustic Testing</text> <text x="130" y="280" font-family="sans-serif" font-size="12" fill="#94a3b8">Pressing an ear to the hive of phonetics.</text> <!-- Mode 3: Spatial Navigation --> <rect x="60" y="315" width="360" height="65" rx="12" fill="#ffffff10"/> <rect x="75" y="328" width="40" height="40" rx="6" fill="#e879f920" stroke="#e879f9" stroke-width="1.5"/> <path d="M85 338 L105 338 L105 358 L85 358 Z M90 343 L100 343 L100 353 L90 353 Z" fill="#e879f9" opacity="0.6"/> <text x="130" y="338" font-family="sans-serif" font-weight="700" font-size="15" fill="#f8fafc">Spatial Navigation</text> <text x="130" y="355" font-family="sans-serif" font-size="12" fill="#94a3b8">Walking the room, feeling for the light switch.</text> <!-- Mode 4: Surface Tension --> <rect x="60" y="390" width="360" height="65" rx="12" fill="#ffffff10"/> <rect x="75" y="403" width="40" height="40" rx="6" fill="#10b98120" stroke="#10b981" stroke-width="1.5"/> <path d="M80 423 Q95 410 110 423" stroke="#10b981" fill="none" stroke-width="2"/> <text x="130" y="413" font-family="sans-serif" font-weight="700" font-size="15" fill="#f8fafc">Surface Tension</text> <text x="130" y="430" font-family="sans-serif" font-size="12" fill="#94a3b8">Waterskiing across literal narrative first.</text> <!-- RIGHT COLUMN: THE SEMANTIC MATRIX --> <rect x="460" y="115" width="380" height="340" rx="16" fill="#ffffff08" stroke="#ffffff10" stroke-width="1"/> <text x="480" y="145" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">II. THE SEMANTIC MATRIX</text> <!-- Matrix Grid --> <line x1="520" y1="410" x2="810" y2="410" stroke="#94a3b8" stroke-width="1" marker-end="url(#arrow)"/> <line x1="520" y1="410" x2="520" y2="180" stroke="#94a3b8" stroke-width="1"/> <text x="815" y="415" font-family="sans-serif" font-size="10" fill="#94a3b8">VALENCE (+)</text> <text x="520" y="170" font-family="sans-serif" font-size="10" fill="#94a3b8" text-anchor="middle">INTENSITY</text> <!-- Data Points --> <!-- Glimmer --> <circle cx="560" cy="360" r="5" fill="#38bdf8" filter="url(#glow)"/> <text x="570" y="365" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Glimmer</text> <text x="570" y="378" font-family="sans-serif" font-size="10" fill="#94a3b8">Fragile / Hopeful</text> <!-- Fire --> <circle cx="620" cy="300" r="6" fill="#f59e0b" filter="url(#glow)"/> <text x="630" y="305" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Fire</text> <text x="630" y="318" font-family="sans-serif" font-size="10" fill="#94a3b8">Primal / Neutral</text> <!-- Blaze --> <circle cx="740" cy="240" r="8" fill="#e879f9" filter="url(#glow)"/> <text x="755" y="245" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Blaze</text> <text x="755" y="258" font-family="sans-serif" font-size="10" fill="#94a3b8">Brilliant / Awe</text> <!-- Inferno --> <circle cx="540" cy="210" r="10" fill="#ef4444" filter="url(#glow)"/> <text x="555" y="215" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Inferno</text> <text x="555" y="228" font-family="sans-serif" font-size="10" fill="#94a3b8">Hellish / Terror</text> <!-- Bottom Info Bar --> <rect x="60" y="480" width="780" height="50" rx="12" fill="url(#accentGrad)" opacity="0.15"/> <rect x="60" y="480" width="780" height="50" rx="12" fill="none" stroke="url(#accentGrad)" stroke-width="1"/> <text x="80" y="510" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">LEXICAL DENSITY:</text> <text x="215" y="510" font-family="sans-serif" font-size="13" fill="#f8fafc">Poetry averages &gt; 0.60 content-to-function word ratio.</text> <!-- Mini Bar Chart --> <text x="580" y="510" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="end">Prose</text> <rect x="590" y="500" width="60" height="12" rx="4" fill="#ffffff20"/> <rect x="590" y="500" width="25" height="12" rx="4" fill="#94a3b8"/> <text x="710" y="510" font-family="sans-serif" font-size="11" fill="#f8fafc" text-anchor="end">Poetry</text> <rect x="720" y="500" width="60" height="12" rx="4" fill="#ffffff20"/> <rect x="720" y="500" width="48" height="12" rx="4" fill="#38bdf8"/> <!-- Decorative Gear Icon (Machine Metaphor) --> <g transform="translate(820, 35) scale(0.8)" opacity="0.5"> <circle cx="20" cy="20" r="15" stroke="#f8fafc" stroke-width="2" fill="none" stroke-dasharray="4 2"/> <circle cx="20" cy="20" r="5" fill="#f8fafc"/> </g> </svg>Poetry: Fundamentals and Craft image 1Poetry: Fundamentals and Craft - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/poetry-fundamentals-and-craft/svg/1Poetry: Fundamentals and Craft diagram 1Poetry: Fundamentals and Craft - Introduction to Literature - diagram 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/poetry-fundamentals-and-craft/svg/2Poetry: Fundamentals and Craft diagram 2Poetry: Fundamentals and Craft - Introduction to Literature - diagram 2https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/poetry-fundamentals-and-craft/svg/3Poetry: Fundamentals and Craft diagram 3Poetry: Fundamentals and Craft - Introduction to Literature - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <linearGradient id="accent-grad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#f59e0b"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> </defs> <!-- Background Layer --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Decorative Header Elements --> <circle cx="50" cy="50" r="100" fill="#38bdf8" fill-opacity="0.05"/> <path d="M 0 80 Q 450 120 900 80" stroke="#ffffff10" fill="none" stroke-width="2"/> <!-- Main Title --> <text x="450" y="60" text-anchor="middle" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="2">THE ARCHITECTURE OF VERSE</text> <text x="450" y="85" text-anchor="middle" font-family="Georgia, serif" font-style="italic" font-size="16" fill="#94a3b8">Meter, Rhyme, and the Engineering of Language</text> <!-- Section 1: The Metrical Foot (Left Panel) --> <rect x="40" y="120" width="260" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="150" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">I. THE METRICAL FOOT</text> <text x="60" y="170" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">The "Atoms" of Rhythmic Pulse</text> <!-- Foot Types --> <g transform="translate(60, 195)"> <!-- Iamb --> <text y="0" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">IAMB</text> <circle cx="80" cy="-5" r="4" fill="#94a3b8"/> <!-- unstressed --> <circle cx="100" cy="-5" r="7" fill="#f59e0b"/> <!-- stressed --> <text y="18" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Rising (x /) - "The heart-beat"</text> <!-- Trochee --> <text y="50" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">TROCHEE</text> <circle cx="80" cy="45" r="7" fill="#e879f9"/> <circle cx="100" cy="45" r="4" fill="#94a3b8"/> <text y="68" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Falling (/ x) - "Driving pulse"</text> <!-- Anapest --> <text y="100" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">ANAPEST</text> <circle cx="80" cy="95" r="4" fill="#94a3b8"/> <circle cx="95" cy="95" r="4" fill="#94a3b8"/> <circle cx="115" cy="95" r="7" fill="#38bdf8"/> <text y="118" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Galloping (x x /) - "Fast pace"</text> <!-- Dactyl --> <text y="150" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">DACTYL</text> <circle cx="80" cy="145" r="7" fill="#38bdf8"/> <circle cx="100" cy="145" r="4" fill="#94a3b8"/> <circle cx="115" cy="145" r="4" fill="#94a3b8"/> <text y="168" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Stately (/ x x) - "Classical epic"</text> </g> <rect x="60" y="400" width="220" height="100" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <text x="70" y="425" font-family="Arial, sans-serif" font-weight="bold" font-size="12" fill="#f59e0b">SCANSION DEFINED</text> <text x="70" y="445" font-family="Arial, sans-serif" font-size="11" fill="#f8fafc">The mapping of stress patterns</text> <text x="70" y="460" font-family="Arial, sans-serif" font-size="11" fill="#f8fafc">to identify the prevailing meter.</text> <text x="70" y="485" font-family="Courier New, monospace" font-size="14" fill="#38bdf8">x / | x / | x /</text> <!-- Section 2: Line Length (Center Panel) --> <rect x="320" y="120" width="260" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="340" y="150" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#e879f9">II. LINE LENGTH</text> <text x="340" y="170" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">The "Molecules" of Verse</text> <!-- Meter Scale --> <g transform="translate(340, 200)"> <line x1="0" y1="0" x2="0" y2="280" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4 4"/> <circle cx="0" cy="20" r="5" fill="#e879f9"/> <text x="15" y="25" font-family="Arial, sans-serif" font-size="13" fill="#f8fafc">Monometer (1)</text> <circle cx="0" cy="60" r="5" fill="#e879f9"/> <text x="15" y="65" font-family="Arial, sans-serif" font-size="13" fill="#f8fafc">Dimeter (2)</text> <circle cx="0" cy="100" r="5" fill="#e879f9"/> <text x="15" y="105" font-family="Arial, sans-serif" font-size="13" fill="#f8fafc">Trimeter (3)</text> <circle cx="0" cy="140" r="5" fill="#e879f9"/> <text x="15" y="145" font-family="Arial, sans-serif" font-size="13" fill="#f8fafc">Tetrameter (4)</text> <!-- Highlighted Pentameter --> <rect x="10" y="165" width="200" height="40" rx="8" fill="#f59e0b20" stroke="#f59e0b50"/> <circle cx="0" cy="185" r="7" fill="#f59e0b"/> <text x="20" y="185" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f59e0b">PENTAMETER (5)</text> <text x="20" y="200" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8">The English Standard (Shakespeare)</text> <circle cx="0" cy="230" r="5" fill="#e879f9"/> <text x="15" y="235" font-family="Arial, sans-serif" font-size="13" fill="#f8fafc">Hexameter (6)</text> <text x="0" y="275" font-family="Arial, sans-serif" font-style="italic" font-size="11" fill="#94a3b8">Named by Foot Type + Number</text> </g> <!-- Section 3: Stanzaic Form (Right Panel) --> <rect x="600" y="120" width="260" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="150" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">III. 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</defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Subtle Grid Lines --> <g stroke="#ffffff08" stroke-width="1"> <line x1="0" y1="100" x2="900" y2="100"/> <line x1="0" y1="460" x2="900" y2="460"/> <line x1="300" y1="100" x2="300" y2="460"/> <line x1="600" y1="100" x2="600" y2="460"/> </g> <!-- Header --> <text x="450" y="55" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="900" fill="#f8fafc" letter-spacing="1">DRAMA &amp; FILM</text> <text x="450" y="80" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="600" fill="#38bdf8" letter-spacing="4">THE ARCHITECTURE OF PERFORMANCE</text> <rect x="400" y="90" width="100" height="3" fill="url(#accentGrad)" rx="1.5"/> <!-- Left Column: The Script (Blueprint) --> <rect x="30" y="120" width="240" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="50" y="150" font-family="sans-serif" font-size="18" 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font-weight="bold" fill="#f8fafc">Primary Text</text> <text x="50" y="340" font-family="sans-serif" font-size="11" fill="#94a3b8">Spoken dialogue and character interaction.</text> <text x="50" y="375" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Secondary Text</text> <text x="50" y="390" font-family="sans-serif" font-size="11" fill="#94a3b8">Stage directions, subtext, and design.</text> <!-- Center Column: Freytag's Pyramid --> <text x="450" y="145" text-anchor="middle" font-family="sans-serif" font-size="18" font-weight="bold" fill="#e879f9">Structure: Freytag’s Pyramid</text> <!-- The Pyramid Path --> <path d="M 330,380 L 400,300 L 450,200 L 500,300 L 570,380" fill="none" stroke="#ffffff20" stroke-width="4" stroke-dasharray="8 4"/> <path d="M 330,380 L 400,300 L 450,200 L 500,300 L 570,380" fill="none" stroke="url(#accentGrad)" stroke-width="3" filter="url(#glow)"/> <!-- Pyramid Points --> <circle cx="330" cy="380" r="5" fill="#38bdf8"/> <circle cx="450" 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font-family="sans-serif" font-size="10" fill="#94a3b8">Law of Dramatic Tension</text> <!-- Right Column: Performance & Film --> <rect x="630" y="120" width="240" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="650" y="150" font-family="sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">Mise-en-scène</text> <!-- Visual Icons --> <g transform="translate(650, 175)"> <circle cx="20" cy="20" r="15" fill="none" stroke="#e879f9" stroke-width="2"/> <line x1="20" y1="5" x2="20" y2="35" stroke="#e879f9" stroke-width="1"/> <line x1="5" y1="20" x2="35" y2="20" stroke="#e879f9" stroke-width="1"/> <text x="45" y="18" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Proxemics</text> <text x="45" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Spatial relationships</text> </g> <g transform="translate(650, 235)"> <rect x="5" y="10" width="30" height="20" rx="4" fill="none" stroke="#f59e0b" stroke-width="2"/> <circle cx="20" cy="20" 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width="840" height="65" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <text x="55" y="513" font-family="sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">The Three Unities</text> <g transform="translate(220, 490)"> <circle cx="20" cy="20" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <text x="45" y="18" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Action</text> <text x="45" y="32" font-family="sans-serif" font-size="10" fill="#94a3b8">One main plot</text> </g> <g transform="translate(440, 490)"> <circle cx="20" cy="20" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="1.5"/> <text x="45" y="18" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Place</text> <text x="45" y="32" font-family="sans-serif" font-size="10" fill="#94a3b8">Single location</text> </g> <g transform="translate(660, 490)"> <circle cx="20" cy="20" r="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <text x="45" y="18" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Time</text> <text x="45" y="32" font-family="sans-serif" font-size="10" fill="#94a3b8">Max 24 hours</text> </g> <!-- Decorative Corner Accents --> <circle cx="0" cy="0" r="40" fill="url(#accentGrad)" opacity="0.1"/> <circle cx="900" cy="560" r="60" fill="#38bdf8" opacity="0.05"/> </svg>Genres: Drama and Film image 1Genres: Drama and Film - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/drama-and-film/svg/1Genres: Drama and Film diagram 1Genres: Drama and Film - Introduction to Literature - diagram 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/drama-and-film/svg/2Genres: Drama and Film diagram 2Genres: Drama and Film - Introduction to Literature - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff05" stroke-width="1"/> </pattern> <pattern id="dots" width="10" height="10" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> </defs> <!-- Background Layer --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <rect width="900" height="120" fill="url(#dots)" opacity="0.5"/> <!-- Header Section --> <rect x="40" y="30" width="820" height="80" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="450" y="72" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="bold" fill="#f8fafc" letter-spacing="1">ASSIGNMENTS &amp; APPLIED ANALYSIS</text> <text x="450" y="95" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="600" fill="#38bdf8" letter-spacing="4">LITERARY DECONSTRUCTION FRAMEWORK</text> <!-- Left Column: Character Analysis --> <rect x="40" y="130" width="400" height="400" rx="16" fill="#ffffff10" stroke="#38bdf833"/> <text x="65" y="165" font-family="sans-serif" font-size="20" font-weight="bold" fill="#f8fafc">Character Architecture</text> <text x="65" y="185" font-family="sans-serif" font-size="12" fill="#94a3b8">The systematic extraction of persona data points.</text> <!-- STEAL Method Visual --> <g transform="translate(65, 210)"> <!-- S --> <rect width="350" height="50" rx="8" fill="#ffffff05"/> <circle cx="25" cy="25" r="15" fill="#f59e0b22" stroke="#f59e0b" stroke-width="1"/> <text x="25" y="30" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f59e0b">S</text> <text x="55" y="22" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Speech</text> <text x="55" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Diction, tone, and subtextual cues.</text> <!-- T --> <g transform="translate(0, 60)"> <rect width="350" height="50" rx="8" fill="#ffffff05"/> <circle cx="25" cy="25" r="15" fill="#38bdf822" stroke="#38bdf8" stroke-width="1"/> <text x="25" y="30" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#38bdf8">T</text> <text x="55" y="22" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Thoughts</text> <text x="55" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Internal monologue vs. public action.</text> </g> <!-- E --> <g transform="translate(0, 120)"> <rect width="350" height="50" rx="8" fill="#ffffff05"/> <circle cx="25" cy="25" r="15" fill="#e879f922" stroke="#e879f9" stroke-width="1"/> <text x="25" y="30" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#e879f9">E</text> <text x="55" y="22" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Effect</text> <text x="55" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Interpersonal friction and social standing.</text> </g> <!-- A --> <g transform="translate(0, 180)"> <rect width="350" height="50" rx="8" fill="#ffffff05"/> <circle cx="25" cy="25" r="15" fill="#10b98122" stroke="#10b981" stroke-width="1"/> <text x="25" y="30" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#10b981">A</text> <text x="55" y="22" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Actions</text> <text x="55" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Moral agency in moments of crisis.</text> </g> <!-- L --> <g transform="translate(0, 240)"> <rect width="350" height="50" rx="8" fill="#ffffff05"/> <circle cx="25" cy="25" r="15" fill="#f43f5e22" stroke="#f43f5e" stroke-width="1"/> <text x="25" y="30" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f43f5e">L</text> <text x="55" y="22" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Looks</text> <text x="55" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Symbolic value of aesthetics and flaws.</text> </g> </g> <!-- Right Column: Close Reading --> <rect x="460" y="130" width="400" height="400" rx="16" fill="#ffffff10" stroke="#e879f933"/> <text x="485" y="165" font-family="sans-serif" font-size="20" font-weight="bold" fill="#f8fafc">Close Reading Loop</text> <text x="485" y="185" font-family="sans-serif" font-size="12" fill="#94a3b8">The recursive micro-analysis of syntax.</text> <!-- Circular Process Diagram --> <g transform="translate(660, 330)"> <circle r="100" fill="none" stroke="#ffffff10" stroke-width="2" stroke-dasharray="8 4"/> <!-- Step 1 --> <g transform="translate(0, -100)"> <circle r="20" fill="#1e1b4b" stroke="#38bdf8" stroke-width="2"/> <text y="5" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#f8fafc">01</text> <text y="-30" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">OBSERVE</text> </g> <!-- Step 2 --> <g transform="translate(100, 0)"> <circle r="20" fill="#1e1b4b" stroke="#38bdf8" stroke-width="2"/> <text y="5" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#f8fafc">02</text> <text x="30" y="5" text-anchor="start" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">ANNOTATE</text> </g> <!-- Step 3 --> <g transform="translate(0, 100)"> <circle r="20" fill="#1e1b4b" stroke="#38bdf8" stroke-width="2"/> <text y="5" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#f8fafc">03</text> <text y="35" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">CONTEXTUALIZE</text> </g> <!-- Step 4 --> <g transform="translate(-100, 0)"> <circle r="20" fill="#1e1b4b" stroke="#38bdf8" stroke-width="2"/> <text y="5" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#f8fafc">04</text> <text x="-30" y="5" text-anchor="end" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">SYNTHESIZE</text> </g> <!-- Center Icon --> <path d="M-15,-15 L15,15 M-15,15 L15,-15" stroke="#e879f9" stroke-width="2" opacity="0.5"/> <circle r="30" fill="none" stroke="#e879f9" stroke-width="1" opacity="0.8"/> <text y="5" text-anchor="middle" font-family="serif" font-size="10" font-style="italic" fill="#e879f9">Deep Dive</text> </g> <!-- Formula Overlay --> <rect x="485" y="460" width="350" height="50" rx="8" fill="#00000033" stroke="#ffffff10"/> <text x="500" y="490" font-family="serif" font-size="16" fill="#f8fafc"> I<tspan baseline-shift="sub" font-size="10">p</tspan> = Σ (w<tspan baseline-shift="sub" font-size="10">i</tspan> · c<tspan baseline-shift="sub" font-size="10">i</tspan>) / W </text> <text x="640" y="490" font-family="sans-serif" font-size="11" fill="#94a3b8">Textual Density Metric</text> <!-- Footer Decorative Elements --> <line x1="40" y1="545" x2="860" y2="545" stroke="url(#accentGrad)" stroke-width="2" opacity="0.5"/> <circle cx="40" cy="545" r="3" fill="#38bdf8"/> <circle cx="860" cy="545" r="3" fill="#e879f9"/> <text x="450" y="555" text-anchor="middle" font-family="sans-serif" font-size="9" fill="#475569" letter-spacing="1">LITERARY ANALYSIS MODULE // VERSION 2.4 // APPLIED HUMANITIES</text> </svg>Assignments and Applied Analysis image 1Assignments and Applied Analysis - Introduction to Literature - image 1https://www.getlykke.com/explore/public/introduction-to-literature-dddd0559-b847-41c2-80b1-3d80bca4bb2b/media/assignments-and-applied-analysis/svg/1Assignments and Applied Analysis diagram 1Assignments and Applied Analysis - Introduction to 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Information</tspan> <tspan x="340" dy="1.2em">democratization at scale.</tspan> </text> <g transform="translate(340, 385)"> <rect width="45" height="45" rx="4" fill="#ffffff11" stroke="#f59e0b" stroke-width="1"/> <text x="22.5" y="30" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="24" font-weight="bold">A</text> <rect x="55" width="45" height="45" rx="4" fill="#ffffff11" stroke="#f59e0b" stroke-width="1"/> <text x="77.5" y="30" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="24" font-weight="bold">g</text> <rect x="110" width="45" height="45" rx="4" fill="#ffffff11" stroke="#f59e0b" stroke-width="1"/> <text x="132.5" y="30" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="24" font-weight="bold">Ω</text> <text x="0" y="65" fill="#94a3b8" font-family="sans-serif" font-size="10" letter-spacing="1">REUSABLE TYPE SLUGS</text> </g> <!-- Panel 3: Reformation (The Fork) --> <rect x="600" y="130" width="260" height="360" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <circle cx="635" cy="165" r="18" fill="#e879f922" stroke="#e879f9" stroke-width="2"/> <path d="M 628 172 L 635 165 L 642 172 M 635 165 L 635 158" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="665" y="170" fill="#e879f9" font-family="sans-serif" font-size="18" font-weight="700">THE FORK</text> <text x="620" y="205" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="700">Protestant Reformation</text> <g transform="translate(620, 230)"> <path d="M 0 40 Q 50 40 100 10 M 0 40 Q 50 40 100 70" fill="none" stroke="#e879f9" stroke-width="2" stroke-dasharray="4 2"/> <circle cx="0" cy="40" r="4" fill="#e879f9"/> <text x="110" y="15" fill="#f8fafc" font-family="sans-serif" font-size="11">Sola Fide</text> <text x="110" y="75" fill="#94a3b8" font-family="sans-serif" font-size="11">Tradition</text> </g> <text x="620" y="330" fill="#94a3b8" font-family="sans-serif" font-size="12"> <tspan x="620" dy="1.2em">A fundamental 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Four-Field Approach diagram 2Introduction to Anthropology and the Four-Field Approach - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="1">RESEARCH METHODS</text> <text x="450" 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fill="#f8fafc">ETIC <tspan font-weight="300" fill="#94a3b8">(The Outsider)</tspan></text> <!-- Left Column: Cultural (The Living Record) --> <rect x="40" y="220" width="400" height="300" rx="20" fill="#ffffff08" stroke="#ffffff10"/> <rect x="40" y="220" width="400" height="50" rx="20" fill="#f59e0b20"/> <text x="60" y="252" font-family="sans-serif" font-size="18" font-weight="700" fill="#f59e0b">CULTURAL: THE LIVING RECORD</text> <!-- Cultural Methods List --> <g transform="translate(60, 290)"> <!-- Participant Observation --> <circle cx="10" cy="10" r="4" fill="#f59e0b"/> <text x="25" y="15" font-family="sans-serif" font-size="14" font-weight="600" fill="#f8fafc">Participant Observation</text> <text x="25" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Immersive engagement and rapport building.</text> <!-- Field Notes --> <circle cx="10" cy="60" r="4" fill="#f59e0b"/> <text x="25" y="65" font-family="sans-serif" font-size="14" font-weight="600" fill="#f8fafc">Qualitative Field Notes</text> <text x="25" y="82" font-family="sans-serif" font-size="11" fill="#94a3b8">Thematic coding of interviews and sensory data.</text> <!-- Mixed Methods --> <circle cx="10" cy="110" r="4" fill="#f59e0b"/> <text x="25" y="115" font-family="sans-serif" font-size="14" font-weight="600" fill="#f8fafc">Mixed Methods (Python/Stats)</text> <text x="25" y="132" font-family="sans-serif" font-size="11" fill="#94a3b8">Quantitative density analysis of cultural nodes.</text> </g> <!-- Python Icon Decoration --> <rect x="340" y="440" width="80" height="60" rx="8" fill="#0f172a" stroke="#f59e0b40"/> <text x="350" y="465" font-family="monospace" font-size="10" fill="#f59e0b">def analyze():</text> <text x="360" y="480" font-family="monospace" font-size="10" fill="#94a3b8"> return nodes</text> <!-- Right Column: Archaeological (The Material Record) --> <rect x="460" y="220" width="400" height="300" rx="20" fill="#ffffff08" stroke="#ffffff10"/> <rect x="460" y="220" width="400" height="50" rx="20" fill="#38bdf820"/> <text x="480" y="252" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">ARCHAEOLOGICAL: MATERIAL RECORD</text> <!-- Archaeological Methods List --> <g transform="translate(480, 290)"> <!-- Excavation --> <rect x="6" cy="6" width="8" height="8" fill="#38bdf8"/> <text x="25" y="15" font-family="sans-serif" font-size="14" font-weight="600" fill="#f8fafc">Systematic Excavation</text> <text x="25" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Controlled recovery of physical remains.</text> <!-- Stratigraphy --> <rect x="6" cy="56" width="8" height="8" fill="#38bdf8"/> <text x="25" y="65" font-family="sans-serif" font-size="14" font-weight="600" fill="#f8fafc">Stratigraphic Analysis</text> <text x="25" y="82" font-family="sans-serif" font-size="11" fill="#94a3b8">Dating via soil layers (Law of Superposition).</text> <!-- Materiality --> <rect x="6" cy="106" width="8" height="8" fill="#38bdf8"/> <text x="25" y="115" font-family="sans-serif" font-size="14" font-weight="600" fill="#f8fafc">Artifact Seriation</text> <text x="25" y="132" font-family="sans-serif" font-size="11" fill="#94a3b8">Tracking stylistic changes over time.</text> </g> <!-- Artifact Icon Decoration --> <path d="M 780 440 L 820 440 L 810 490 L 790 490 Z" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <line x1="780" y1="455" x2="820" y2="455" stroke="#38bdf840" stroke-width="1"/> <line x1="785" y1="470" x2="815" y2="470" stroke="#38bdf840" stroke-width="1"/> <!-- Footer: Cultural Relativism --> <path d="M 40 535 L 860 535" stroke="#ffffff20" stroke-width="1" stroke-dasharray="4 4"/> <text x="450" y="550" text-anchor="middle" font-family="sans-serif" font-size="11" font-style="italic" fill="#94a3b8"> The Principle of Cultural Relativism: Suspending ethnocentrism for objective data collection. </text> <!-- Connecting Bridge --> <path d="M 440 370 Q 450 370 460 370" stroke="#e879f9" stroke-width="2" fill="none" marker-end="url(#arrowhead)"/> <circle cx="450" cy="370" r="20" fill="#1e1b4b" stroke="#e879f9" stroke-width="1"/> <text x="450" y="374" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#e879f9">HOLISM</text> </svg>Research Methods: Cultural and Archaeological image 1Research Methods: Cultural and Archaeological - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/anthropological-methods/svg/1Research Methods: Cultural and Archaeological diagram 1Research Methods: Cultural and Archaeological - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/anthropological-methods/svg/2Research Methods: Cultural and Archaeological diagram 2Research Methods: Cultural and Archaeological - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="32" font-weight="800" letter-spacing="1">CULTURE CONCEPT &amp; THEORIES OF CHANGE</text> <path d="M 350 65 L 550 65" stroke="#38bdf8" stroke-width="2" stroke-linecap="round"/> <text x="450" y="85" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="400" letter-spacing="2">THE ANTHROPOLOGICAL OPERATING SYSTEM</text> <!-- Left Column: The Three-Tiered Structure --> <rect x="40" y="120" width="280" height="340" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="150" fill="#f59e0b" font-family="sans-serif" font-size="18" font-weight="700">THE THREE-TIERED STRUCTURE</text> <!-- Superstructure --> <rect x="60" y="170" width="240" height="75" rx="8" fill="#f59e0b15" stroke="#f59e0b40"/> <text x="75" y="195" fill="#f59e0b" font-family="sans-serif" font-size="14" font-weight="700">SUPERSTRUCTURE</text> <text x="75" y="215" fill="#cbd5e1" font-family="sans-serif" font-size="11">Mental &amp; Ideological: Religion, values,</text> <text x="75" y="230" fill="#cbd5e1" font-family="sans-serif" font-size="11">worldviews, and symbolic meaning.</text> <!-- Structure --> <rect x="60" y="255" width="240" height="75" rx="8" fill="#e879f915" stroke="#e879f940"/> <text x="75" y="280" fill="#e879f9" font-family="sans-serif" font-size="14" font-weight="700">STRUCTURE</text> <text x="75" y="300" fill="#cbd5e1" font-family="sans-serif" font-size="11">Social Organization: Kinship, political</text> <text x="75" y="315" fill="#cbd5e1" font-family="sans-serif" font-size="11">systems, and institutional frameworks.</text> <!-- Infrastructure --> <rect x="60" y="340" width="240" height="75" rx="8" fill="#38bdf815" stroke="#38bdf840"/> <text x="75" y="365" fill="#38bdf8" font-family="sans-serif" font-size="14" font-weight="700">INFRASTRUCTURE</text> <text x="75" y="385" fill="#cbd5e1" font-family="sans-serif" font-size="11">Material Base: Technology, economy,</text> <text x="75" y="400" fill="#cbd5e1" font-family="sans-serif" font-size="11">environment, and production modes.</text> <!-- Right Side: Homeyness vs Winkiness --> <rect x="340" y="120" width="520" height="160" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="380" cy="160" r="25" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <path d="M 370 165 Q 380 145 390 165" fill="none" stroke="#38bdf8" stroke-width="2"/> <path d="M 370 160 L 390 160" stroke="#38bdf8" stroke-width="1" opacity="0.5"/> <text x="420" y="155" fill="#38bdf8" font-family="sans-serif" font-size="18" font-weight="700">HOMEYNESS (The Unmarked State)</text> <text x="420" y="180" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="600">The "Water" in which the fish swims.</text> <text x="420" y="200" fill="#94a3b8" font-family="sans-serif" font-size="12">Linked to Bourdieu's Habitus. It is invisible, providing</text> <text x="420" y="215" fill="#94a3b8" font-family="sans-serif" font-size="12">ontological security and a sense of "naturalness."</text> <rect x="420" y="230" width="80" height="20" rx="4" fill="#38bdf820"/> <text x="460" y="244" text-anchor="middle" fill="#38bdf8" font-family="sans-serif" font-size="10" font-weight="700">INVISIBILITY</text> <rect x="510" y="230" width="80" height="20" rx="4" fill="#38bdf820"/> <text x="550" y="244" text-anchor="middle" fill="#38bdf8" font-family="sans-serif" font-size="10" font-weight="700">HABITUS</text> <rect x="340" y="300" width="520" height="160" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="380" cy="340" r="25" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <path d="M 370 340 Q 380 325 390 340" fill="none" stroke="#e879f9" stroke-width="2"/> <path d="M 370 340 Q 380 355 390 340" fill="none" stroke="#e879f9" stroke-width="2"/> <circle cx="380" cy="340" r="4" fill="#e879f9"/> <path d="M 370 330 L 375 335 M 385 335 L 390 330" stroke="#e879f9" stroke-width="2"/> <text x="420" y="335" fill="#e879f9" font-family="sans-serif" font-size="18" font-weight="700">WINKINESS (The Symbolic Web)</text> <text x="420" y="360" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="600">Geertz's "Thick Description".</text> <text x="420" y="380" fill="#94a3b8" font-family="sans-serif" font-size="12">The layers of meaning, irony, and intent. A wink is not</text> <text x="420" y="395" fill="#94a3b8" font-family="sans-serif" font-size="12">just a twitch; it is a shared secret in a web of significance.</text> <rect x="420" y="410" width="110" height="20" rx="4" fill="#e879f920"/> <text x="475" y="424" text-anchor="middle" fill="#e879f9" font-family="sans-serif" font-size="10" font-weight="700">SEMIOTIC ANALYSIS</text> <rect x="540" y="410" width="110" height="20" rx="4" fill="#e879f920"/> <text x="595" y="424" text-anchor="middle" fill="#e879f9" font-family="sans-serif" font-size="10" font-weight="700">THICK DESCRIPTION</text> <!-- Bottom: Enculturation --> <rect x="40" y="480" width="820" height="50" rx="12" fill="#ffffff05" stroke="#ffffff10"/> <text x="60" y="510" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="700">ENCULTURATION:</text> <text x="185" y="510" fill="#94a3b8" font-family="sans-serif" font-size="12">The transmission of culture through social learning.</text> <g transform="translate(500, 503)"> <circle cx="0" cy="0" r="12" fill="#38bdf820" stroke="#38bdf8"/> <path d="M -4 0 L 4 0 M 0 -4 L 0 4" stroke="#38bdf8" stroke-width="1.5"/> <text x="18" y="4" fill="#38bdf8" font-family="sans-serif" font-size="11" font-weight="700">VERTICAL (Parents)</text> <circle cx="130" cy="0" r="12" fill="#e879f920" stroke="#e879f9"/> <path d="M 126 0 L 134 0" stroke="#e879f9" stroke-width="1.5"/> <text x="148" y="4" fill="#e879f9" font-family="sans-serif" font-size="11" font-weight="700">HORIZONTAL (Peers)</text> <circle cx="260" cy="0" r="12" fill="#f59e0b20" stroke="#f59e0b"/> <path d="M 257 -3 L 263 3 M 263 -3 L 257 3" stroke="#f59e0b" stroke-width="1.5"/> <text x="278" y="4" fill="#f59e0b" font-family="sans-serif" font-size="11" font-weight="700">OBLIQUE (Institutions)</text> </g> <!-- Decorative accents --> <circle cx="860" cy="40" r="60" fill="#38bdf808"/> <circle cx="40" cy="520" r="40" fill="#e879f908"/> <path d="M 880 100 L 900 100 M 890 90 L 890 110" stroke="#ffffff20" stroke-width="1"/> </svg>Culture Concept and Theories of Change image 1Culture Concept and Theories of Change - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/culture-concept-theory/svg/1Culture Concept and Theories of Change diagram 1Culture Concept and Theories of Change - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/culture-concept-theory/svg/2Culture Concept and Theories of Change diagram 2Culture Concept and Theories of Change - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> 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font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">THE FOUR FORCES</text> <!-- Force 1: Mutation --> <g transform="translate(60, 175)"> <circle cx="20" cy="20" r="20" fill="#38bdf820" stroke="#38bdf8" stroke-width="1"/> <path d="M 12 12 L 28 28 M 28 12 L 12 28" stroke="#38bdf8" stroke-width="2"/> <text x="50" y="15" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Mutation</text> <text x="50" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">The source of new alleles.</text> </g> <!-- Force 2: Selection --> <g transform="translate(60, 245)"> <circle cx="20" cy="20" r="20" fill="#e879f920" stroke="#e879f9" stroke-width="1"/> <circle cx="20" cy="20" r="8" fill="none" stroke="#e879f9" stroke-width="2"/> <path d="M 20 5 L 20 10 M 20 30 L 20 35 M 5 20 L 10 20 M 30 20 L 35 20" stroke="#e879f9" stroke-width="2"/> <text x="50" y="15" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Natural Selection</text> <text x="50" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Differential fitness success.</text> </g> <!-- Force 3: Drift --> <g transform="translate(60, 315)"> <circle cx="20" cy="20" r="20" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1"/> <circle cx="15" cy="15" r="2" fill="#f59e0b"/> <circle cx="25" cy="18" r="2" fill="#f59e0b"/> <circle cx="18" cy="26" r="2" fill="#f59e0b"/> <text x="50" y="15" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Genetic Drift</text> <text x="50" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Random allele fluctuations.</text> </g> <!-- Force 4: Flow --> <g transform="translate(60, 385)"> <circle cx="20" cy="20" r="20" fill="#10b98120" stroke="#10b981" stroke-width="1"/> <path d="M 10 20 H 30 M 25 15 L 30 20 L 25 25" fill="none" stroke="#10b981" stroke-width="2"/> <text x="50" y="15" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Gene Flow</text> <text x="50" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Migration between groups.</text> </g> <!-- Main Content: Timeline --> <rect x="320" y="120" width="540" height="290" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="340" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">HOMININ LINEAGE TIMELINE</text> <!-- Timeline Path --> <path d="M 360 320 Q 450 320 450 240 T 540 240 T 630 240 T 820 240" fill="none" stroke="#ffffff20" stroke-width="4" stroke-dasharray="8 4"/> <!-- Timeline Nodes --> <g transform="translate(360, 320)"> <circle r="6" fill="#f59e0b" filter="url(#glow)"/> <text y="25" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc" font-weight="bold">Ardipithecus</text> <text y="40" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">~4.4 MYA</text> </g> <g transform="translate(480, 240)"> <circle r="6" fill="#f59e0b" filter="url(#glow)"/> <text y="-25" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc" font-weight="bold">Australopithecus</text> <text y="-12" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">~3.5 MYA</text> </g> <g transform="translate(600, 240)"> <circle r="6" fill="#f59e0b" filter="url(#glow)"/> <text y="25" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc" font-weight="bold">Homo erectus</text> <text y="40" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">~1.8 MYA</text> </g> <g transform="translate(800, 240)"> <circle r="8" fill="#38bdf8" filter="url(#glow)"/> <text y="-25" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#f8fafc" font-weight="bold">Homo sapiens</text> <text y="-12" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#38bdf8">PRESENT</text> </g> <!-- Genetics Section --> <rect x="320" y="430" width="540" height="100" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="340" y="460" font-family="sans-serif" font-weight="700" font-size="16" fill="#e879f9">THE MOLECULAR BLUEPRINT</text> <!-- Hardy Weinberg --> <g transform="translate(340, 480)"> <rect width="220" height="35" rx="8" fill="#00000030"/> <text x="110" y="24" text-anchor="middle" font-family="serif" font-style="italic" font-size="18" fill="#f8fafc">p² + 2pq + q² = 1</text> <text x="240" y="15" font-family="sans-serif" font-size="11" fill="#94a3b8">Hardy-Weinberg Equilibrium:</text> <text x="240" y="30" font-family="sans-serif" font-size="11" fill="#94a3b8">The null model for evolution.</text> </g> <!-- Decorative Accents --> <circle cx="850" cy="50" r="30" fill="none" stroke="#ffffff10" stroke-width="2"/> <circle cx="850" cy="50" r="15" fill="none" stroke="#ffffff05" stroke-width="1"/> <path d="M 820 50 L 880 50 M 850 20 L 850 80" stroke="#ffffff08" stroke-width="1"/> <!-- Bottom Label --> <text x="860" y="545" text-anchor="end" font-family="sans-serif" font-size="10" fill="#ffffff30" letter-spacing="2">ANTHROPOLOGY SERIES // VOL 01</text> </svg>Biological Evolution and Early Human Evidence image 1Biological Evolution and Early Human Evidence - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/biological-evolution/svg/1Biological Evolution and Early Human Evidence diagram 1Biological Evolution and Early Human Evidence - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/biological-evolution/svg/2Biological Evolution and Early Human Evidence diagram 2Biological Evolution and Early Human Evidence - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" 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width="260" height="380" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="160" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">CEREBRAL RUBICON</text> <text x="60" y="180" font-family="sans-serif" font-size="12" fill="#94a3b8">The threshold of brain encephalization.</text> <!-- Brain Size Comparison --> <circle cx="100" cy="240" r="22" fill="#334155" stroke="#94a3b8"/> <text x="135" y="235" font-family="sans-serif" font-size="11" fill="#f8fafc" font-weight="bold">A. afarensis</text> <text x="135" y="250" font-family="sans-serif" font-size="10" fill="#94a3b8">~450 cc</text> <circle cx="100" cy="300" r="28" fill="#1e293b" stroke="#38bdf8" stroke-width="2"/> <text x="145" y="295" font-family="sans-serif" font-size="11" fill="#f8fafc" font-weight="bold">H. habilis</text> <text x="145" y="310" font-family="sans-serif" font-size="10" fill="#38bdf8">~610 cc</text> <circle cx="100" cy="375" r="38" fill="#1e293b" stroke="#f59e0b" stroke-width="2"/> <text 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340 Q 500 380 470 390" fill="none" stroke="#94a3b8" stroke-width="2"/> <path d="M 420 390 Q 380 380 370 345" fill="none" stroke="#94a3b8" stroke-width="2"/> <path d="M 380 300 Q 400 270 430 255" fill="none" stroke="#94a3b8" stroke-width="2"/> <text x="340" y="450" font-family="sans-serif" font-size="12" fill="#94a3b8" width="220"> <tspan x="340" dy="1.2em">Cultural innovation drives biological</tspan> <tspan x="340" dy="1.2em">change, which in turn enables more</tspan> <tspan x="340" dy="1.2em">complex cultural adaptations.</tspan> </text> <!-- Right Panel: Expensive Tissue Hypothesis --> <rect x="600" y="130" width="260" height="380" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="620" y="160" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">EXPENSIVE TISSUE</text> <!-- Scale Visual --> <line x1="650" y1="320" x2="810" y2="320" stroke="#94a3b8" stroke-width="2"/> <path d="M 730 320 L 710 350 L 750 350 Z" fill="#334155"/> <!-- Left Side of Scale (Brain) 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Agriculture --> <rect x="665" y="230" width="185" height="260" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <circle cx="757" cy="270" r="25" fill="#22c55e20" /> <!-- Field Icon --> <rect x="742" y="260" width="30" height="20" fill="none" stroke="#22c55e" stroke-width="1.5"/> <line x1="752" y1="260" x2="752" y2="280" stroke="#22c55e" stroke-width="1"/> <line x1="762" y1="260" x2="762" y2="280" stroke="#22c55e" stroke-width="1"/> <text x="757" y="315" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="bold" font-size="18">AGRICULTURE</text> <text x="757" y="340" text-anchor="middle" fill="#22c55e" font-family="sans-serif" font-size="12" font-weight="bold">"The Urban Revolution"</text> <text x="680" y="370" fill="#94a3b8" font-family="sans-serif" font-size="12"> <tspan x="680" dy="1.4em">• Intensive cultivation</tspan> <tspan x="680" dy="1.4em">• Massive food surplus</tspan> <tspan x="680" dy="1.4em">• State formation</tspan> <tspan x="680" dy="1.4em">• High stratification</tspan> </text> <!-- Bottom Scale/Arrow --> <defs> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="#ffffff30" /> </marker> </defs> <line x1="50" y1="530" x2="840" y2="530" stroke="#ffffff30" stroke-width="2" marker-end="url(#arrowhead)"/> <text x="50" y="550" fill="#94a3b8" font-family="sans-serif" font-size="10" font-weight="bold">LOW SOCIAL STRATIFICATION</text> <text x="850" y="550" text-anchor="end" fill="#94a3b8" font-family="sans-serif" font-size="10" font-weight="bold">HIGH SOCIAL STRATIFICATION</text> <!-- Substantivist vs Formalist Label --> <rect x="300" y="505" width="300" height="24" rx="12" fill="#38bdf820" stroke="#38bdf840"/> <text x="450" y="521" text-anchor="middle" fill="#38bdf8" font-family="sans-serif" font-size="11" font-weight="bold">SUBSTANTIVIST (Social Logic) vs. FORMALIST (Market Logic)</text> </svg>Work, Life, and Value: Economic Anthropology image 1Work, Life, and Value: Economic Anthropology - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/economic-anthropology/svg/1Work, Life, and Value: Economic Anthropology diagram 1Work, Life, and Value: Economic Anthropology - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/economic-anthropology/svg/2Work, Life, and Value: Economic Anthropology diagram 2Work, Life, and Value: Economic Anthropology - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="600" letter-spacing="4">POLITICAL ANTHROPOLOGY</text> <text x="450" y="90" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="32" font-weight="800">Authority, Decisions, &amp; Power</text> <line x1="350" y1="110" x2="550" y2="110" stroke="url(#accentGrad)" stroke-width="3" stroke-linecap="round"/> <!-- Main Comparison Panels --> <!-- LEFT PANEL: ACEPHALOUS --> <rect x="40" y="140" width="400" height="380" rx="20" fill="#ffffff08" stroke="#ffffff15"/> <text x="65" y="180" fill="#38bdf8" font-family="sans-serif" font-size="22" font-weight="700">Acephalous Societies</text> <text x="65" y="205" fill="#94a3b8" font-family="sans-serif" font-size="14">"Headless" • Bands &amp; Tribes • Egalitarian</text> <!-- Icon: Consensus Circle --> <g transform="translate(340, 180)"> <circle cx="0" cy="0" r="30" fill="none" stroke="#38bdf8" stroke-dasharray="4 4"/> <circle cx="0" cy="-30" r="6" fill="#38bdf8"/> <circle cx="26" cy="-15" r="6" fill="#38bdf8"/> <circle cx="26" cy="15" r="6" fill="#38bdf8"/> <circle cx="0" cy="30" r="6" fill="#38bdf8"/> <circle cx="-26" cy="15" r="6" fill="#38bdf8"/> <circle cx="-26" cy="-15" r="6" fill="#38bdf8"/> </g> <!-- Leveling Mechanisms Card --> <rect x="60" y="240" width="360" height="130" rx="12" fill="#ffffff05" stroke="#38bdf830"/> <text x="75" y="265" fill="#f8fafc" font-family="sans-serif" font-size="15" font-weight="600">Social Leveling Mechanisms</text> <text x="75" y="290" fill="#94a3b8" font-family="sans-serif" font-size="13">• Gossip &amp; Shaming: Public criticism</text> <text x="75" y="310" fill="#94a3b8" font-family="sans-serif" font-size="13">• Meat-Sharing: Preventing food control</text> <text x="75" y="330" fill="#94a3b8" font-family="sans-serif" font-size="13">• Reverse Dominance: Collective control</text> <text x="75" y="350" fill="#f59e0b" font-family="sans-serif" font-size="12" font-style="italic">Example: !Kung San "Insulting the Meat"</text> <text x="65" y="410" fill="#f8fafc" font-family="sans-serif" font-size="16" font-weight="600">Influence vs. Authority</text> <text x="65" y="435" fill="#94a3b8" font-family="sans-serif" font-size="13" width="350"> <tspan x="65" dy="0">Power is diffused. Leaders have the ability to</tspan> <tspan x="65" dy="18">persuade (influence) but lack the recognized</tspan> <tspan x="65" dy="18">right to command (authority).</tspan> </text> <!-- RIGHT PANEL: CENTRALIZED --> <rect x="460" y="140" width="400" height="380" rx="20" fill="#ffffff08" stroke="#ffffff15"/> <text x="485" y="180" fill="#f59e0b" font-family="sans-serif" font-size="22" font-weight="700">Centralized Societies</text> <text x="485" y="205" fill="#94a3b8" font-family="sans-serif" font-size="14">States &amp; Chiefdoms • Stratified • Bureaucratic</text> <!-- Icon: Hierarchy Pyramid --> <g transform="translate(760, 180)"> <path d="M0 -35 L35 25 L-35 25 Z" fill="none" stroke="#f59e0b" stroke-width="2"/> <line x1="-20" y1="-10" x2="20" y2="-10" stroke="#f59e0b" stroke-width="1"/> <line x1="-28" y1="10" x2="28" y2="10" stroke="#f59e0b" stroke-width="1"/> <circle cx="0" cy="-20" r="4" fill="#f59e0b"/> </g> <!-- Structure Card --> <rect x="480" y="240" width="360" height="130" rx="12" fill="#ffffff05" stroke="#f59e0b30"/> <text x="495" y="265" fill="#f8fafc" font-family="sans-serif" font-size="15" font-weight="600">Institutionalized Power</text> <rect x="495" y="280" width="165" height="75" rx="8" fill="#ffffff05"/> <text x="505" y="300" fill="#f59e0b" font-family="sans-serif" font-size="13" font-weight="600">Chiefdoms</text> <text x="505" y="320" fill="#94a3b8" font-family="sans-serif" font-size="11">Hereditary Rank</text> <text x="505" y="335" fill="#94a3b8" font-family="sans-serif" font-size="11">Kinship-based</text> <rect x="665" y="280" width="165" height="75" rx="8" fill="#ffffff05"/> <text x="675" y="300" fill="#f59e0b" font-family="sans-serif" font-size="13" font-weight="600">States</text> <text x="675" y="320" fill="#94a3b8" font-family="sans-serif" font-size="11">Bureaucratic</text> <text x="675" y="335" fill="#94a3b8" font-family="sans-serif" font-size="11">Class-based</text> <text x="485" y="410" fill="#f8fafc" font-family="sans-serif" font-size="16" font-weight="600">Agency vs. Structure</text> <text x="485" y="435" fill="#94a3b8" font-family="sans-serif" font-size="13"> <tspan x="485" dy="0">The tension between individual capacity to act</tspan> <tspan x="485" dy="18">(agency) and the formal social arrangements</tspan> <tspan x="485" dy="18">that limit behavior (structure).</tspan> </text> <!-- Bottom Label --> <rect x="350" y="500" width="200" height="30" rx="15" fill="url(#accentGrad)" opacity="0.2"/> <text x="450" y="520" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">THE SPECTRUM OF POLITICAL ORGANIZATION</text> </svg>Authority, Decisions, and Power: Political Anthropology image 1Authority, Decisions, and Power: Political Anthropology - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/political-anthropology/svg/1Authority, Decisions, and Power: Political Anthropology diagram 1Authority, Decisions, and Power: Political Anthropology - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/political-anthropology/svg/2Authority, Decisions, and Power: Political Anthropology diagram 2Authority, Decisions, and Power: Political Anthropology - Anthropology - diagram 2https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/political-anthropology/svg/3Authority, Decisions, and Power: Political Anthropology diagram 3Authority, Decisions, and Power: Political Anthropology - Anthropology - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Subtle Grid Lines --> <path d="M 0 100 L 900 100 M 0 460 L 900 460" stroke="#ffffff08" stroke-width="1"/> <path d="M 450 100 L 450 460" stroke="#ffffff08" stroke-width="1"/> <!-- Header --> <text x="450" y="60" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="32" font-weight="bold" letter-spacing="1">SOCIAL INEQUALITY &amp; GLOBAL MIGRATION</text> <text x="450" y="85" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="300" letter-spacing="4">A SYSTEMIC FEEDBACK LOOP OF GLOBALIZATION</text> <!-- Left Panel: Push Factors (Inequality) --> <rect x="40" y="120" width="380" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="155" fill="#f59e0b" font-family="sans-serif" font-size="18" font-weight="bold">THE ARCHITECTURE OF INEQUALITY</text> <text x="60" y="175" fill="#94a3b8" font-family="sans-serif" font-size="12">Systemic drivers in the country of origin</text> <!-- Inequality Dimensions --> <g transform="translate(60, 200)"> <!-- Economic --> <circle cx="15" cy="15" r="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <path d="M 10 15 L 20 15 M 15 10 L 15 20" stroke="#f59e0b" stroke-width="2"/> <text x="40" y="12" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="bold">Economic Disparity</text> <text x="40" y="28" fill="#94a3b8" font-family="sans-serif" font-size="11">Wealth concentration &amp; Gini imbalance</text> <!-- Social --> <g transform="translate(0, 50)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <rect x="10" y="10" width="10" height="10" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="40" y="12" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="bold">Social Access</text> <text x="40" y="28" fill="#94a3b8" font-family="sans-serif" font-size="11">Unequal education &amp; healthcare (HDI)</text> </g> <!-- Political --> <g transform="translate(0, 100)"> <circle cx="15" cy="15" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="1.5"/> <path d="M 8 18 L 15 8 L 22 18 Z" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="40" y="12" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="bold">Political Power</text> <text x="40" y="28" fill="#94a3b8" font-family="sans-serif" font-size="11">Differential access to legal protections</text> </g> </g> <!-- Right Panel: Pull Factors (Migration) --> <rect x="480" y="120" width="380" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="500" y="155" fill="#38bdf8" font-family="sans-serif" font-size="18" font-weight="bold">MECHANICS OF MIGRATION</text> <text x="500" y="175" fill="#94a3b8" font-family="sans-serif" font-size="12">Aspirational leaps and survival strategies</text> <!-- Pull Factors List --> <g transform="translate(500, 200)"> <rect width="340" height="40" rx="8" fill="#ffffff05"/> <text x="15" y="25" fill="#f8fafc" font-family="sans-serif" font-size="13">Labor Demand &amp; Global Markets</text> <circle cx="320" cy="20" r="4" fill="#38bdf8"/> <rect y="50" width="340" height="40" rx="8" fill="#ffffff05"/> <text x="15" y="75" fill="#f8fafc" font-family="sans-serif" font-size="13">Political Stability &amp; Civil Liberties</text> <circle cx="320" cy="70" r="4" fill="#38bdf8"/> <rect y="100" width="340" height="40" rx="8" fill="#ffffff05"/> <text x="15" y="125" fill="#f8fafc" font-family="sans-serif" font-size="13">Family Reunification &amp; Networks</text> <circle cx="320" cy="120" r="4" fill="#38bdf8"/> </g> <!-- Center Connection --> <path d="M 420 280 Q 450 280 480 280" stroke="#f8fafc30" stroke-width="2" stroke-dasharray="8 4"/> <path d="M 475 275 L 485 280 L 475 285 Z" fill="#f8fafc30"/> <text x="450" y="270" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="10" font-weight="bold">PUSH-PULL</text> <!-- Bottom Section: Gini Coefficient Visualization --> <rect x="40" y="460" width="820" height="80" rx="16" fill="#ffffff10"/> <!-- Mini Lorenz Curve Graph --> <g transform="translate(60, 475)"> <rect width="50" height="50" fill="none" stroke="#94a3b8" stroke-width="1"/> <line x1="0" y1="50" x2="50" y2="0" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2 2"/> <path d="M 0 50 Q 40 50 50 0" fill="#f59e0b30" stroke="#f59e0b" stroke-width="2"/> <text x="65" y="20" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="bold">The Gini Coefficient (G)</text> <text x="65" y="40" fill="#94a3b8" font-family="sans-serif" font-size="12">G = A / (A + B) — Measuring the gap between equality and reality.</text> </g> <!-- Python Snippet Visual --> <g transform="translate(550, 475)"> <rect width="290" height="50" rx="4" fill="#00000040"/> <text x="10" y="20" fill="#38bdf8" font-family="monospace" font-size="10">def calculate_migration_pressure(df):</text> <text x="10" y="35" fill="#e879f9" font-family="monospace" font-size="10"> MPI = alpha * (Unemp) + beta * (1/Inc)</text> </g> <!-- Decorative Elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#e879f9" stroke-width="0.5" opacity="0.5"/> <circle cx="850" cy="50" r="20" fill="none" stroke="#e879f9" stroke-width="0.5" opacity="0.3"/> <circle cx="50" cy="510" r="40" fill="none" stroke="#38bdf8" stroke-width="0.5" opacity="0.2"/> </svg>Social Inequality and Global Migration image 1Social Inequality and Global Migration - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/inequality-and-migration/svg/1Social Inequality and Global Migration diagram 1Social Inequality and Global Migration - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/inequality-and-migration/svg/2Social Inequality and Global Migration diagram 2Social Inequality and Global Migration - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Decorative Header Line --> <rect x="40" y="85" width="820" height="1" fill="url(#accentGrad)" opacity="0.5"/> <!-- Title Section --> <text x="40" y="55" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">FORMING FAMILY</text> <text x="310" y="53" font-family="sans-serif" font-weight="400" font-size="16" fill="#94a3b8">Kinship, Gender, and Sexuality: The Social Operating System</text> <!-- Column 1: Kinship Foundations --> <rect x="40" y="110" width="260" height="410" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="145" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">I. KINSHIP TYPES</text> <text x="60" y="165" font-family="sans-serif" font-size="12" fill="#94a3b8">The logic of social connection</text> <!-- Consanguineal --> <circle cx="75" cy="210" r="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2"/> <path d="M70 210 L80 210 M75 205 L75 215" stroke="#f59e0b" stroke-width="2"/> <text x="100" y="205" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Consanguineal</text> <text x="100" y="220" font-family="sans-serif" font-size="11" fill="#94a3b8">Related by "blood" or descent.</text> <!-- Affinal --> <circle cx="68" cy="270" r="12" fill="none" stroke="#38bdf8" stroke-width="2"/> <circle cx="82" cy="270" r="12" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="100" y="265" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Affinal</text> <text x="100" y="280" font-family="sans-serif" font-size="11" fill="#94a3b8">Related by marriage/contract.</text> <!-- Fictive --> <path d="M75 315 L85 335 L65 335 Z" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="100" y="325" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Fictive</text> <text x="100" y="340" font-family="sans-serif" font-size="11" fill="#94a3b8">Chosen family &amp; ritual bonds.</text> <!-- Column 2: Descent Systems --> <rect x="320" y="110" width="260" height="410" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="340" y="145" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">II. DESCENT LOGIC</text> <!-- Patrilineal --> <g transform="translate(340, 180)"> <rect width="220" height="60" rx="8" fill="#ffffff05"/> <circle cx="25" cy="30" r="12" fill="#38bdf820" stroke="#38bdf8"/> <path d="M25 22 V38 M20 27 L25 22 L30 27" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="50" y="25" font-family="sans-serif" font-weight="600" font-size="13" fill="#f8fafc">Patrilineal</text> <text x="50" y="42" font-family="sans-serif" font-size="11" fill="#94a3b8">Traced through the male line.</text> </g> <!-- Matrilineal --> <g transform="translate(340, 255)"> <rect width="220" height="60" rx="8" fill="#ffffff05"/> <circle cx="25" cy="30" r="12" fill="#e879f920" stroke="#e879f9"/> <path d="M25 22 V38 M20 33 L25 38 L30 33" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="50" y="25" font-family="sans-serif" font-weight="600" font-size="13" fill="#f8fafc">Matrilineal</text> <text x="50" y="42" font-family="sans-serif" font-size="11" fill="#94a3b8">Traced through the female line.</text> </g> <!-- Bilateral --> <g transform="translate(340, 330)"> <rect width="220" height="60" rx="8" fill="#ffffff05"/> <path d="M15 30 L25 20 L35 30 L25 40 Z" fill="#f59e0b20" stroke="#f59e0b"/> <text x="50" y="25" font-family="sans-serif" font-weight="600" font-size="13" fill="#f8fafc">Bilateral</text> <text x="50" y="42" font-family="sans-serif" font-size="11" fill="#94a3b8">Traced through both parents.</text> </g> <!-- Column 3: Alliance & Rules --> <rect x="600" y="110" width="260" height="410" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="145" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">III. ALLIANCE THEORY</text> <g transform="translate(620, 180)"> <text x="0" y="0" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Exogamy</text> <text x="0" y="18" font-family="sans-serif" font-size="12" fill="#94a3b8">Marrying outside the group.</text> <path d="M0 30 H220" stroke="#ffffff20" stroke-dasharray="4"/> <text x="0" y="60" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Endogamy</text> <text x="0" y="78" font-family="sans-serif" font-size="12" fill="#94a3b8">Marrying within the group.</text> <path d="M0 90 H220" stroke="#ffffff20" stroke-dasharray="4"/> <text x="0" y="120" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Incest Taboo</text> <text x="0" y="138" font-family="sans-serif" font-size="12" fill="#94a3b8" width="200">Universal cultural prohibition.</text> </g> <!-- Bottom Formula/Code Visual --> <rect x="620" y="360" width="220" height="130" rx="8" fill="#00000030"/> <text x="635" y="385" font-family="monospace" font-size="11" fill="#38bdf8"># Kinship Distance</text> <text x="635" y="405" font-family="monospace" font-size="11" fill="#f8fafc">def calculate_r(path):</text> <text x="635" y="420" font-family="monospace" font-size="11" fill="#f8fafc"> return sum(0.5 ** L)</text> <text x="635" y="450" font-family="serif" font-style="italic" font-size="14" fill="#94a3b8">r = Σ (0.5)^L</text> <text x="635" y="475" font-family="sans-serif" font-size="10" fill="#64748b">Coefficient of Relationship</text> <!-- Decorative Elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#ffffff05" stroke-width="8"/> <circle cx="850" cy="50" r="15" fill="none" stroke="#ffffff05" stroke-width="4"/> <path d="M40 540 H860" stroke="#ffffff10" stroke-width="2"/> <text x="450" y="545" font-family="sans-serif" font-size="10" fill="#475569" text-anchor="middle">ANTHROPOLOGICAL PERSPECTIVES ON SOCIAL STRUCTURE</text> </svg>Forming Family: Kinship, Gender, and Sexuality image 1Forming Family: Kinship, Gender, and Sexuality - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/kinship-gender-sexuality/svg/1Forming Family: Kinship, Gender, and Sexuality diagram 1Forming Family: Kinship, Gender, and Sexuality - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/kinship-gender-sexuality/svg/2Forming Family: Kinship, Gender, and Sexuality diagram 2Forming Family: Kinship, Gender, and Sexuality - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="-0.5">RELIGION, ART, &amp; EXPRESSIVE CULTURE</text> <text x="40" y="85" font-family="sans-serif" font-size="14" fill="#94a3b8" font-weight="400">The primary mechanisms through which human beings construct meaning and negotiate power.</text> <line x1="40" y1="105" x2="860" y2="105" stroke="#ffffff20" stroke-width="1"/> <!-- Left Column: The Architecture of Ritual --> <rect x="40" y="130" width="400" height="390" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="160" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">THE ARCHITECTURE OF RITUAL</text> <text x="60" y="180" font-family="sans-serif" font-size="12" fill="#94a3b8">The Tripartite Structure (Van Gennep &amp; Turner)</text> <!-- Ritual Steps --> <!-- Step 1 --> <circle cx="80" cy="225" r="18" fill="#ffffff15" stroke="#f59e0b" stroke-width="2"/> <text x="76" y="230" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f59e0b">1</text> <text x="110" y="220" font-family="sans-serif" font-size="15" font-weight="600" fill="#f8fafc">Separation</text> <text x="110" y="235" font-family="sans-serif" font-size="11" fill="#94a3b8">Stripping of previous social identity.</text> <line x1="80" y1="243" x2="80" y2="277" stroke="#ffffff20" stroke-dasharray="4 2"/> <!-- Step 2 --> <circle cx="80" cy="300" r="18" fill="#ffffff15" stroke="#e879f9" stroke-width="2" filter="url(#glow)"/> <text x="76" y="305" font-family="sans-serif" font-size="14" font-weight="bold" fill="#e879f9">2</text> <text x="110" y="295" font-family="sans-serif" font-size="15" font-weight="600" fill="#f8fafc">Liminality</text> <text x="110" y="310" font-family="sans-serif" font-size="11" fill="#94a3b8">The "Betwixt and Between" phase. Status: None.</text> <line x1="80" y1="318" x2="80" y2="352" stroke="#ffffff20" stroke-dasharray="4 2"/> <!-- Step 3 --> <circle cx="80" cy="375" r="18" fill="#ffffff15" stroke="#38bdf8" stroke-width="2"/> <text x="76" y="380" font-family="sans-serif" font-size="14" font-weight="bold" fill="#38bdf8">3</text> <text x="110" y="370" font-family="sans-serif" font-size="15" font-weight="600" fill="#f8fafc">Incorporation</text> <text x="110" y="385" font-family="sans-serif" font-size="11" fill="#94a3b8">Re-entry into society with a new status.</text> <!-- Communitas Box --> <rect x="60" y="420" width="360" height="80" rx="12" fill="#e879f910" stroke="#e879f930"/> <text x="75" y="445" font-family="sans-serif" font-size="14" font-weight="bold" fill="#e879f9">COMMUNITAS</text> <text x="75" y="465" font-family="sans-serif" font-size="11" fill="#f8fafc">Intense togetherness and equality emerging</text> <text x="75" y="480" font-family="sans-serif" font-size="11" fill="#f8fafc">during the liminal phase, transcending hierarchy.</text> <!-- Right Column: Symbolism & Semiotics --> <rect x="460" y="130" width="400" height="240" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="480" y="160" font-family="sans-serif" font-size="18" font-weight="700" fill="#f59e0b">SYMBOLIC DENSITY</text> <!-- Formula Visualization --> <rect x="480" y="180" width="360" height="60" rx="8" fill="#00000030"/> <text x="500" y="215" font-family="serif" font-size="20" fill="#f8fafc" font-style="italic">Δs = ∫ (M · R) dC</text> <text x="680" y="205" font-family="sans-serif" font-size="10" fill="#94a3b8">M: Multivocality</text> <text x="680" y="220" font-family="sans-serif" font-size="10" fill="#94a3b8">R: Resonance</text> <text x="680" y="235" font-family="sans-serif" font-size="10" fill="#94a3b8">C: Cultural Field</text> <!-- Multivocality Diagram --> <circle cx="530" cy="310" r="25" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2"/> <text x="515" y="315" font-family="sans-serif" font-size="10" font-weight="bold" fill="#f59e0b">SYMBOL</text> <!-- Radiating meanings --> <line x1="555" y1="310" x2="590" y2="290" stroke="#f59e0b" stroke-width="1"/> <text x="600" y="288" font-family="sans-serif" font-size="11" fill="#f8fafc">History</text> <line x1="555" y1="310" x2="590" y2="310" stroke="#f59e0b" stroke-width="1"/> <text x="600" y="315" font-family="sans-serif" font-size="11" fill="#f8fafc">Fertility</text> <line x1="555" y1="310" x2="590" y2="330" stroke="#f59e0b" stroke-width="1"/> <text x="600" y="340" font-family="sans-serif" font-size="11" fill="#f8fafc">Law</text> <text x="670" y="315" font-family="sans-serif" font-size="12" font-style="italic" fill="#94a3b8">"Multivocality: One form,</text> <text x="670" y="330" font-family="sans-serif" font-size="12" font-style="italic" fill="#94a3b8">many meanings."</text> <!-- Bottom Right: Semiotics Table --> <rect x="460" y="390" width="400" height="130" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="480" y="420" font-family="sans-serif" font-size="14" font-weight="700" fill="#38bdf8">SEMIOTIC LOGIC</text> <line x1="480" y1="435" x2="840" y2="435" stroke="#ffffff10"/> <text x="480" y="455" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">SIGNIFIER</text> <text x="600" y="455" font-family="sans-serif" font-size="12" fill="#94a3b8">The physical form (e.g., a sound or image)</text> <text x="480" y="485" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">SIGNIFIED</text> <text x="600" y="485" font-family="sans-serif" font-size="12" fill="#94a3b8">The mental concept or cultural meaning</text> <text x="480" y="505" font-family="sans-serif" font-size="10" font-style="italic" fill="#38bdf8">The link between them is arbitrary and culturally defined.</text> <!-- Decorative Corner Accents --> <path d="M860 40 L880 40 L880 60" fill="none" stroke="#f59e0b" stroke-width="2"/> <path d="M40 520 L20 520 L20 500" fill="none" stroke="#38bdf8" stroke-width="2"/> </svg>Religion, Art, and Expressive Culture image 1Religion, Art, and Expressive Culture - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/religion-and-expressive-culture/svg/1Religion, Art, and Expressive Culture diagram 1Religion, Art, and Expressive Culture - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/religion-and-expressive-culture/svg/2Religion, Art, and Expressive Culture diagram 2Religion, Art, and Expressive Culture - Anthropology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="40" y="60" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-0.5">MEDICAL ANTHROPOLOGY</text> <text x="40" y="90" font-family="Arial, sans-serif" font-weight="400" font-size="18" fill="#38bdf8" letter-spacing="1">INDIGENOUS EXPERIENCES &amp; DECOLONIAL HEALTH</text> <line x1="40" y1="110" x2="860" y2="110" stroke="#ffffff20" stroke-width="1"/> <!-- Section 1: Biocultural Synthesis --> <rect x="40" y="135" width="260" height="220" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <circle cx="75" cy="170" r="18" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2"/> <path d="M 68 170 L 82 170 M 75 163 L 75 177" stroke="#f59e0b" stroke-width="2"/> <text x="105" y="175" font-family="Arial, sans-serif" font-weight="700" font-size="18" fill="#f59e0b">BIOCULTURAL</text> <text x="60" y="210" font-family="Arial, sans-serif" font-size="13" fill="#f8fafc" font-weight="600">The Multi-Scalar System</text> <text x="60" y="235" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8"> <tspan x="60" dy="0">Rejects Cartesian dualism. Health</tspan> <tspan x="60" dy="18">is a feedback loop between</tspan> <tspan x="60" dy="18">biological plasticity and cultural</tspan> <tspan x="60" dy="18">adaptation. Pathogens meet</tspan> <tspan x="60" dy="18">socioeconomic reality.</tspan> </text> <path d="M 60 330 Q 170 310 280 330" fill="none" stroke="#f59e0b40" stroke-width="2" stroke-dasharray="4 2"/> <!-- Section 2: The Syndemic Model --> <rect x="320" y="135" width="260" height="220" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <path d="M 345 180 L 360 155 L 375 180 Z" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="385" y="175" font-family="Arial, sans-serif" font-weight="700" font-size="18" fill="#e879f9">SYNDEMICS</text> <text x="340" y="210" font-family="Arial, sans-serif" font-size="13" fill="#f8fafc" font-weight="600">Biological Social Suffering</text> <rect x="340" y="225" width="220" height="100" rx="8" fill="#00000030"/> <text x="350" y="245" font-family="Arial, sans-serif" font-size="12" fill="#e879f9" font-weight="bold">Disease A + Disease B</text> <text x="350" y="265" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Interacting with:</text> <text x="350" y="285" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">Structural Inequality</text> <text x="350" y="305" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">Environmental Stress</text> <!-- Section 3: OCAP Principles --> <rect x="600" y="135" width="260" height="220" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <rect x="620" y="155" width="30" height="30" rx="4" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <text x="660" y="175" font-family="Arial, sans-serif" font-weight="700" font-size="18" fill="#38bdf8">OCAP DATA</text> <g font-family="Arial, sans-serif" font-size="12" font-weight="bold"> <rect x="620" y="200" width="105" height="25" rx="4" fill="#38bdf815"/> <text x="628" y="217" fill="#38bdf8">OWNERSHIP</text> <rect x="735" y="200" width="105" height="25" rx="4" fill="#38bdf815"/> <text x="743" y="217" fill="#38bdf8">CONTROL</text> <rect x="620" y="235" width="105" height="25" rx="4" fill="#38bdf815"/> <text x="628" y="252" fill="#38bdf8">ACCESS</text> <rect x="735" y="235" width="105" height="25" rx="4" fill="#38bdf815"/> <text x="743" y="252" fill="#38bdf8">POSSESSION</text> </g> <text x="620" y="285" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8"> <tspan x="620" dy="0">Dismantling "Helicopter</tspan> <tspan x="620" dy="18">Research" through Indigenous</tspan> <tspan x="620" dy="18">Data Sovereignty.</tspan> </text> <!-- Bottom Section: Structural Violence --> <rect x="40" y="375" width="820" height="150" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="70" y="410" font-family="Arial, sans-serif" font-weight="700" font-size="20" fill="#f8fafc">STRUCTURAL VIOLENCE &amp; WEATHERING</text> <!-- Visualizing the "Weathering" concept --> <path d="M 70 480 L 150 470 L 230 485 L 310 460 L 390 475 L 470 440 L 550 455 L 630 420" fill="none" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <circle cx="630" cy="420" r="5" fill="#f59e0b"/> <text x="450" y="410" font-family="Arial, sans-serif" font-size="13" fill="#94a3b8"> <tspan x="450" dy="25">Social arrangements that harm populations by preventing basic needs.</tspan> <tspan x="450" dy="20">"Weathering" is the premature biological aging caused by the cumulative</tspan> <tspan x="450" dy="20">impact of social, economic, and political adversity (Paul Farmer).</tspan> </text> <!-- Decorative Elements --> <circle cx="840" cy="60" r="20" fill="#e879f920"/> <circle cx="840" cy="60" r="10" fill="#e879f940"/> <g opacity="0.4"> <circle cx="800" cy="500" r="3" fill="#38bdf8"/> <circle cx="820" cy="500" r="3" fill="#38bdf8"/> <circle cx="840" cy="500" r="3" fill="#38bdf8"/> </g> <!-- Footer Label --> <rect x="720" y="520" width="140" height="24" rx="12" fill="#38bdf8"/> <text x="790" y="537" font-family="Arial, sans-serif" font-weight="bold" font-size="11" fill="#0f172a" text-anchor="middle">SOCIAL JUSTICE FOCUS</text> </svg>Medical Anthropology and Indigenous Experiences image 1Medical Anthropology and Indigenous Experiences - Anthropology - image 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/medical-and-indigenous-anthropology/svg/1Medical Anthropology and Indigenous Experiences diagram 1Medical Anthropology and Indigenous Experiences - Anthropology - diagram 1https://www.getlykke.com/explore/public/anthropology-a4bd31d3-9ba4-46c3-8304-912d8aac0a6c/media/medical-and-indigenous-anthropology/svg/2Medical Anthropology and Indigenous Experiences diagram 2Medical Anthropology and Indigenous Experiences - Anthropology - diagram 2https://www.getlykke.com/explore/public/principles-of-macroeconomics-0555c62a-12dd-4b40-b6fe-b39608198a3f2026-04-20T05:05:43.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="cardGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#ffffff1a"/> <stop offset="100%" stop-color="#ffffff05"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background Layer --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="40" y="50" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-0.025em">FOUNDATIONS OF MACROECONOMICS</text> <text x="40" y="75" font-family="sans-serif" font-size="14" fill="#94a3b8" font-weight="500" text-transform="uppercase" letter-spacing="0.1em">The Study of Choice Under Constraint</text> <line x1="40" y1="95" x2="860" y2="95" stroke="#334155" stroke-width="1"/> <!-- Left Column: The Economic Problem --> <rect x="40" y="115" width="260" height="200" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="60" y="145" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">The Axiom of Scarcity</text> <text x="60" y="170" font-family="sans-serif" font-size="12" fill="#cbd5e1" width="220"> <tspan x="60" dy="0">A permanent, structural gap between</tspan> <tspan x="60" dy="18">limitless human wants and the</tspan> <tspan x="60" dy="18">finite resources of our world.</tspan> </text> <!-- Scarcity Visual --> <circle cx="100" cy="260" r="30" fill="none" stroke="#f59e0b" stroke-width="2" stroke-dasharray="4 2"/> <text x="100" y="264" font-family="sans-serif" font-size="10" fill="#f59e0b" text-anchor="middle" font-weight="bold">RESOURCES</text> <path d="M 140 260 L 170 260" stroke="#94a3b8" stroke-width="2" marker-end="url(#arrow)"/> <circle cx="210" cy="260" r="45" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="210" y="264" font-family="sans-serif" font-size="10" fill="#e879f9" text-anchor="middle" font-weight="bold">WANTS</text> <!-- Center: Factors of Production --> <text x="320" y="135" font-family="sans-serif" font-size="16" font-weight="700" fill="#f8fafc">Factors of Production</text> <!-- Land --> <rect x="320" y="150" width="120" height="75" rx="12" fill="#ffffff08" stroke="#10b98133" stroke-width="1"/> <text x="335" y="175" font-family="sans-serif" font-size="14" font-weight="700" fill="#10b981">LAND</text> <text x="335" y="195" font-family="sans-serif" font-size="11" fill="#94a3b8">Natural Resources</text> <text x="335" y="210" font-family="sans-serif" font-size="10" fill="#10b981" font-weight="bold">Return: Rent</text> <!-- Labor --> <rect x="450" y="150" width="120" height="75" rx="12" fill="#ffffff08" stroke="#38bdf833" stroke-width="1"/> <text x="465" y="175" font-family="sans-serif" font-size="14" font-weight="700" fill="#38bdf8">LABOR</text> <text 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fill="#f59e0b"/> <text x="67" y="-25" font-family="sans-serif" font-size="10" fill="#f59e0b">C (Inefficient)</text> <circle cx="180" cy="-100" r="4" fill="#e879f9"/> <text x="187" y="-105" font-family="sans-serif" font-size="10" fill="#e879f9">D (Unattainable)</text> </g> <!-- PPF Description --> <text x="400" y="370" font-family="sans-serif" font-size="18" font-weight="700" fill="#f8fafc">Production Possibilities Frontier (PPF)</text> <text x="400" y="395" font-family="sans-serif" font-size="12" fill="#cbd5e1"> <tspan x="400" dy="0">• Points on the curve represent maximum productive efficiency.</tspan> <tspan x="400" dy="22">• The concave shape illustrates the Law of Increasing Opportunity Costs.</tspan> <tspan x="400" dy="22">• Outward shifts represent economic growth via technology or resources.</tspan> <tspan x="400" dy="22">• Trade-offs: Moving from A to B increases consumer goods but reduces capital.</tspan> </text> <!-- Marginal Analysis Badge --> <rect x="680" y="465" width="160" height="40" rx="20" fill="#38bdf822" stroke="#38bdf8" stroke-width="1"/> <text x="760" y="490" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8" text-anchor="middle">MARGINAL ANALYSIS: MB ≥ MC</text> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="#e879f9" fill-opacity="0.1"/> <circle cx="850" cy="50" r="15" fill="#e879f9" fill-opacity="0.2"/> </svg>Foundations of Macroeconomics and Choice image 1Foundations of Macroeconomics and Choice - Principles of Macroeconomics - image 1https://www.getlykke.com/explore/public/principles-of-macroeconomics-0555c62a-12dd-4b40-b6fe-b39608198a3f/media/foundations-of-macroeconomics/svg/1Foundations of Macroeconomics and Choice diagram 1Foundations of Macroeconomics and Choice - Principles of Macroeconomics - diagram 1https://www.getlykke.com/explore/public/principles-of-macroeconomics-0555c62a-12dd-4b40-b6fe-b39608198a3f/media/foundations-of-macroeconomics/svg/2Foundations of Macroeconomics and Choice diagram 2Foundations of Macroeconomics and Choice - Principles of Macroeconomics - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="32" letter-spacing="1">MARKET MECHANICS &amp; MACROECONOMIC GOALS</text> <text x="450" y="85" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="400" letter-spacing="2">THE INTEGRATED SYSTEM OF NATIONAL ECONOMIC HEALTH</text> <rect x="400" y="95" width="100" height="3" fill="#f59e0b" rx="1.5"/> <!-- Left Card: Micro Foundations --> <rect x="40" y="130" width="260" height="380" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="60" y="165" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="18">01. MICRO-FOUNDATIONS</text> <text x="60" y="185" fill="#94a3b8" font-family="sans-serif" font-size="12">The Market Mechanism</text> <!-- Supply/Demand Mini Graph --> <g transform="translate(70, 210)"> <line x1="0" y1="100" x2="120" y2="100" stroke="#94a3b8" stroke-width="1"/> <line x1="0" y1="0" x2="0" y2="100" stroke="#94a3b8" stroke-width="1"/> <!-- Demand --> <path d="M 10 10 L 110 90" stroke="#38bdf8" stroke-width="3" fill="none"/> <text x="115" y="95" fill="#38bdf8" font-family="sans-serif" font-size="10" font-weight="bold">D</text> <!-- Supply --> <path d="M 10 90 L 110 10" stroke="#f59e0b" stroke-width="3" fill="none"/> <text x="115" y="15" fill="#f59e0b" font-family="sans-serif" font-size="10" font-weight="bold">S</text> <!-- Equilibrium --> <circle cx="60" cy="50" r="4" fill="#f8fafc" filter="url(#glow)"/> <line x1="60" y1="50" x2="60" y2="100" stroke="#f8fafc" stroke-dasharray="3,3" stroke-width="1"/> <line x1="0" y1="50" x2="60" y2="50" stroke="#f8fafc" stroke-dasharray="3,3" stroke-width="1"/> <text x="65" y="45" fill="#f8fafc" font-family="serif" font-style="italic" font-size="12">E*</text> </g> <text x="60" y="345" fill="#f8fafc" font-family="sans-serif" font-weight="600" font-size="14">Equilibrium Price (P*)</text> <text x="60" y="365" fill="#94a3b8" font-family="sans-serif" font-size="12" width="220">The point where Quantity Supplied</text> <text x="60" y="380" fill="#94a3b8" font-family="sans-serif" font-size="12">equals Quantity Demanded.</text> <rect x="60" y="405" width="220" height="85" rx="8" fill="#38bdf810"/> <text x="75" y="430" fill="#38bdf8" font-family="serif" font-style="italic" font-size="14">Qd = α - βP</text> <text x="75" y="455" fill="#f59e0b" font-family="serif" font-style="italic" font-size="14">Qs = γ + δP</text> <text x="75" y="480" fill="#f8fafc" font-family="sans-serif" font-weight="bold" font-size="11">SOLVE: α - βP = γ + δP</text> <!-- Middle Card: GDP & Growth --> <rect x="320" y="130" width="260" height="380" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="340" y="165" fill="#4ade80" font-family="sans-serif" font-weight="700" font-size="18">02. ECONOMIC OUTPUT</text> <text x="340" y="185" fill="#94a3b8" font-family="sans-serif" font-size="12">Gross Domestic Product (GDP)</text> <!-- GDP Components Visual --> <g transform="translate(340, 210)"> <rect x="0" y="0" width="220" height="30" rx="4" fill="#4ade8020" stroke="#4ade80" stroke-width="1"/> <text x="110" y="20" text-anchor="middle" fill="#f8fafc" font-family="serif" font-weight="bold" font-size="16">GDP = C + I + G + NX</text> <g transform="translate(0, 50)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8"/> <text x="15" y="20" text-anchor="middle" fill="#38bdf8" font-weight="bold" font-size="12">C</text> <text x="40" y="18" fill="#f8fafc" font-size="12" font-weight="600">Consumption</text> <circle cx="15" cy="55" r="15" fill="#e879f920" stroke="#e879f9"/> <text x="15" y="60" text-anchor="middle" fill="#e879f9" font-weight="bold" font-size="12">I</text> <text x="40" y="58" fill="#f8fafc" font-size="12" font-weight="600">Investment</text> <circle cx="15" cy="95" r="15" fill="#f59e0b20" stroke="#f59e0b"/> <text x="15" y="100" text-anchor="middle" fill="#f59e0b" font-weight="bold" font-size="12">G</text> <text x="40" y="98" fill="#f8fafc" font-size="12" font-weight="600">Government</text> <circle cx="15" cy="135" r="15" fill="#94a3b820" stroke="#94a3b8"/> <text x="15" y="140" text-anchor="middle" fill="#94a3b8" font-weight="bold" font-size="12">NX</text> <text x="40" y="138" fill="#f8fafc" font-size="12" font-weight="600">Net Exports</text> </g> </g> <rect x="340" y="405" width="220" height="85" rx="8" fill="#4ade8010"/> <text x="355" y="430" fill="#4ade80" font-family="sans-serif" font-weight="bold" font-size="13">REAL VS. NOMINAL</text> <text x="355" y="450" fill="#94a3b8" font-family="sans-serif" font-size="11">Nominal: Current Prices</text> <text x="355" y="465" fill="#94a3b8" font-family="sans-serif" font-size="11">Real: Base Year (Inflation Adjusted)</text> <text x="355" y="482" fill="#f8fafc" font-family="serif" font-size="11">Deflator = (Nominal / Real) × 100</text> <!-- Right Card: Human Capital --> <rect x="600" y="130" width="260" height="380" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="620" y="165" fill="#e879f9" font-family="sans-serif" font-weight="700" font-size="18">03. HUMAN CAPITAL</text> <text x="620" y="185" fill="#94a3b8" font-family="sans-serif" font-size="12">Unemployment &amp; Stability</text> <!-- Stability Gauge --> <g transform="translate(650, 210)"> <path d="M 0 80 A 60 60 0 0 1 120 80" fill="none" stroke="#ffffff15" stroke-width="12" stroke-linecap="round"/> <path d="M 0 80 A 60 60 0 0 1 40 25" fill="none" stroke="#e879f9" stroke-width="12" stroke-linecap="round" filter="url(#glow)"/> <text x="60" y="75" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="20">4.2%</text> <text x="60" y="95" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="10">UNEMPLOYMENT</text> </g> <g transform="translate(620, 320)"> <text x="0" y="20" fill="#f8fafc" font-family="sans-serif" font-weight="600" font-size="14">The Three Pillars of Stability</text> <rect x="0" y="35" width="220" height="1" fill="#ffffff15"/> <circle cx="10" cy="55" r="4" fill="#e879f9"/> <text x="25" y="60" fill="#f8fafc" font-size="12">Frictional: Job searching</text> <circle cx="10" cy="80" r="4" fill="#e879f9"/> <text x="25" y="85" fill="#f8fafc" font-size="12">Structural: Skill mismatch</text> <circle cx="10" cy="105" r="4" fill="#e879f9"/> <text x="25" y="110" fill="#f8fafc" font-size="12">Cyclical: Economic downturns</text> </g> <rect x="620" y="445" width="220" height="45" rx="8" fill="#e879f910"/> <text x="635" y="465" fill="#e879f9" font-family="sans-serif" font-weight="bold" font-size="11">PRICE STABILITY</text> <text x="635" y="480" fill="#94a3b8" font-family="sans-serif" font-size="11">Target Inflation: ~2% per annum</text> <!-- Bottom Connector --> <path d="M 170 510 L 170 530 L 730 530 L 730 510" fill="none" stroke="#ffffff15" stroke-width="2"/> <circle cx="450" cy="530" r="20" fill="#1e1b4b" stroke="#ffffff15" stroke-width="2"/> <text x="450" y="535" text-anchor="middle" fill="#f59e0b" font-family="sans-serif" font-weight="bold" font-size="14">Σ</text> <!-- Footer --> <text x="860" y="545" text-anchor="end" fill="#ffffff20" font-family="sans-serif" font-size="10" font-weight="bold">WIKI.ECON.4.1 // SYSTEM OVERVIEW</text> </svg>Market Mechanics and Macroeconomic Goals image 1Market Mechanics and Macroeconomic Goals - Principles of Macroeconomics - image 1https://www.getlykke.com/explore/public/principles-of-macroeconomics-0555c62a-12dd-4b40-b6fe-b39608198a3f/media/market-mechanics-and-goals/svg/1Market Mechanics and Macroeconomic Goals diagram 1Market Mechanics and Macroeconomic Goals - Principles of Macroeconomics - diagram 1https://www.getlykke.com/explore/public/principles-of-macroeconomics-0555c62a-12dd-4b40-b6fe-b39608198a3f/media/market-mechanics-and-goals/svg/2Market Mechanics and Macroeconomic Goals diagram 2Market Mechanics and Macroeconomic Goals - Principles of Macroeconomics - diagram 2https://www.getlykke.com/explore/public/principles-of-macroeconomics-0555c62a-12dd-4b40-b6fe-b39608198a3f/media/market-mechanics-and-goals/svg/3Market Mechanics and Macroeconomic Goals diagram 3Market Mechanics and Macroeconomic Goals - Principles of Macroeconomics - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">Macroeconomic Models &amp; Perspectives</text> <text x="40" y="85" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">THE AGGREGATE DEMAND / AGGREGATE SUPPLY FRAMEWORK</text> <rect x="40" y="100" width="120" height="4" rx="2" fill="#38bdf8"/> <!-- Left Panel: Aggregate Demand --> <rect x="40" y="130" width="260" height="390" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="165" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">Aggregate Demand (AD)</text> <text x="60" y="185" font-family="sans-serif" font-size="12" fill="#94a3b8">Total spending on domestic goods</text> <text x="60" y="220" font-family="serif" font-style="italic" font-size="18" fill="#f8fafc">AD = C + I + G + (X - M)</text> <!-- AD Components --> <g transform="translate(60, 250)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1"/> <text x="15" y="20" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#38bdf8" font-weight="bold">C</text> <text x="45" y="12" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="600">Consumption</text> <text x="45" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Wealth effect &amp; 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Fiscal Policy - Principles of Macroeconomics - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="cardGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#ffffff15"/> <stop offset="100%" stop-color="#ffffff05"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#334155" fill-opacity="0.5"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Decorative Header Line --> <rect x="40" y="70" width="820" height="1" fill="#334155"/> <rect x="40" y="70" width="150" height="2" fill="#38bdf8"/> <!-- Title Section --> <text x="40" y="50" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">GLOBALIZATION <tspan fill="#38bdf8">&amp;</tspan> ECONOMIC EDUCATION</text> <text x="860" y="50" font-family="sans-serif" font-size="14" font-weight="600" fill="#94a3b8" text-anchor="end">THE DUAL-AXIS EVOLUTION</text> <!-- Left Panel: Physical Integration --> <rect x="40" y="90" width="400" height="360" rx="16" fill="url(#cardGrad)" stroke="#ffffff10"/> <text x="60" y="125" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">PHYSICAL INTEGRATION</text> <text x="60" y="145" font-family="sans-serif" font-size="12" fill="#94a3b8">The mechanics of international trade and capital.</text> <!-- Comparative Advantage Graphic --> <rect x="60" y="170" width="360" height="80" rx="8" fill="#00000030"/> <text x="75" y="195" font-family="sans-serif" font-weight="700" font-size="14" 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stroke-dasharray="5,5"/> <path d="M-50 0 L50 0 M0 -50 L0 50" stroke="#334155" stroke-width="1"/> </g> <!-- Floating Tags --> <g transform="translate(40, 420)"> <rect width="90" height="20" rx="10" fill="#38bdf820" stroke="#38bdf8" stroke-width="1"/> <text x="45" y="14" font-family="sans-serif" font-size="10" fill="#38bdf8" text-anchor="middle">LIBERALIZATION</text> </g> <g transform="translate(140, 420)"> <rect width="90" height="20" rx="10" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1"/> <text x="45" y="14" font-family="sans-serif" font-size="10" fill="#f59e0b" text-anchor="middle">CAPITAL FLOW</text> </g> <g transform="translate(670, 420)"> <rect width="90" height="20" rx="10" fill="#e879f920" stroke="#e879f9" stroke-width="1"/> <text x="45" y="14" font-family="sans-serif" font-size="10" fill="#e879f9" text-anchor="middle">KNOWLEDGE SPILL</text> </g> <g transform="translate(770, 420)"> <rect width="90" height="20" rx="10" fill="#38bdf820" stroke="#38bdf8" stroke-width="1"/> 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2https://www.getlykke.com/explore/public/principles-of-macroeconomics-0555c62a-12dd-4b40-b6fe-b39608198a3f/media/globalization-and-oer-integration/svg/3Globalization and the Future of Economic Education diagram 3Globalization and the Future of Economic Education - Principles of Macroeconomics - diagram 3https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff202026-04-20T05:02:34.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bgGradient" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bgGradient)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">GEOLOGY &amp; THE SCIENTIFIC METHOD</text> <text x="450" y="75" text-anchor="middle" font-family="Arial, sans-serif" font-size="14" fill="#94a3b8" letter-spacing="3">DECODING THE 4.54 BILLION YEAR NARRATIVE</text> <line x1="350" y1="85" x2="550" y2="85" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2"/> <!-- Left Column: The Dual Pillars --> <g transform="translate(40, 110)"> <rect width="260" height="190" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="20" y="30" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">PHYSICAL GEOLOGY</text> <text x="20" y="52" font-family="Arial, sans-serif" font-size="13" fill="#94a3b8">The "Mechanics" of the Planet</text> <!-- Physical Icon --> <path d="M 200 25 L 230 75 L 170 75 Z" fill="none" stroke="#38bdf8" stroke-width="2"/> <circle cx="200" cy="65" r="8" fill="#38bdf8" fill-opacity="0.3"/> <text x="20" y="90" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">• Plate Tectonics &amp; Volcanism</text> <text x="20" y="110" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">• Mineralogy &amp; Petrology</text> <text x="20" y="130" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">• Rock Formation &amp; Erosion</text> <rect x="20" y="150" width="220" height="25" rx="4" fill="#38bdf820"/> <text x="130" y="167" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-style="italic" fill="#38bdf8">Focus: Materials &amp; Processes</text> </g> <g transform="translate(40, 320)"> <rect width="260" height="190" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="20" y="30" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">HISTORICAL GEOLOGY</text> <text x="20" y="52" font-family="Arial, sans-serif" font-size="13" fill="#94a3b8">The Chronology of Earth</text> <!-- Historical Icon --> <path d="M 180 35 H 220 M 180 45 H 220 M 180 55 H 220" stroke="#f59e0b" stroke-width="3" stroke-linecap="round"/> <circle cx="200" cy="65" r="10" fill="none" stroke="#f59e0b" stroke-width="1.5"/> <text x="20" y="90" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">• Stratigraphy (Rock Layers)</text> <text x="20" y="110" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">• Paleontology (Fossils)</text> <text x="20" y="130" font-family="Arial, sans-serif" font-size="12" fill="#f8fafc">• Biological Evolution</text> <rect x="20" y="150" width="220" height="25" rx="4" fill="#f59e0b20"/> <text x="130" y="167" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-style="italic" fill="#f59e0b">Focus: Origin &amp; Development</text> </g> <!-- Center Column: Scientific Method --> <g transform="translate(320, 110)"> <rect width="260" height="400" rx="16" fill="#ffffff05" stroke="#e879f9" stroke-dasharray="4 4"/> <text x="130" y="35" text-anchor="middle" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#e879f9">SCIENTIFIC METHOD</text> <!-- Workflow Steps --> <g transform="translate(30, 60)"> <circle cx="20" cy="20" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="20" y="25" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">1</text> <text x="45" y="18" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">OBSERVATION</text> <text x="45" y="32" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Identify natural phenomena</text> <line x1="20" y1="35" x2="20" y2="65" stroke="#e879f9" stroke-width="1" stroke-dasharray="2 2"/> <g transform="translate(0, 70)"> <circle cx="20" cy="20" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="20" y="25" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">2</text> <text x="45" y="18" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">HYPOTHESIS</text> <text x="45" y="32" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Tentative explanation</text> </g> <line x1="20" y1="105" x2="20" y2="135" stroke="#e879f9" stroke-width="1" stroke-dasharray="2 2"/> <g transform="translate(0, 140)"> <circle cx="20" cy="20" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="20" y="25" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">3</text> <text x="45" y="18" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">TESTING</text> <text x="45" y="32" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Data &amp; Field Mapping</text> </g> <line x1="20" y1="175" x2="20" y2="205" stroke="#e879f9" stroke-width="1" stroke-dasharray="2 2"/> <g transform="translate(0, 210)"> <circle cx="20" cy="20" r="15" fill="#e879f9" stroke="#e879f9" stroke-width="2"/> <text x="20" y="25" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#0f172a">4</text> <text x="45" y="18" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">THEORY</text> <text x="45" y="32" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Confirmed explanation</text> </g> </g> <rect x="20" y="320" width="220" height="60" rx="8" fill="#ffffff10"/> <text x="130" y="340" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#e879f9">ABDUCTIVE REASONING</text> <text x="130" y="358" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">"Inference to the best explanation"</text> <text x="130" y="372" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">used for ancient events.</text> </g> <!-- Right Column: Earth System Science --> <g transform="translate(600, 110)"> <rect width="260" height="400" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="130" y="35" text-anchor="middle" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#4ade80">EARTH SYSTEM (ESS)</text> <!-- Sphere Grid --> <g transform="translate(30, 60)"> <!-- Geosphere --> <rect width="90" height="70" rx="8" fill="#38bdf815" stroke="#38bdf8" stroke-width="1"/> <text x="45" y="35" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#f8fafc">GEOSPHERE</text> <text x="45" y="50" text-anchor="middle" font-family="Arial, sans-serif" font-size="9" fill="#94a3b8">Solid Earth</text> <!-- Atmosphere --> <rect x="110" width="90" height="70" rx="8" fill="#e879f915" stroke="#e879f9" stroke-width="1"/> <text x="155" y="35" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#f8fafc">ATMOSPHERE</text> <text x="155" y="50" text-anchor="middle" font-family="Arial, sans-serif" font-size="9" fill="#94a3b8">Gases</text> <!-- Hydrosphere --> <rect y="85" width="90" height="70" rx="8" fill="#38bdf815" stroke="#38bdf8" stroke-width="1"/> <text x="45" y="120" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#f8fafc">HYDROSPHERE</text> <text x="45" y="135" text-anchor="middle" font-family="Arial, sans-serif" font-size="9" fill="#94a3b8">Water/Ice</text> <!-- Biosphere --> <rect x="110" y="85" width="90" height="70" rx="8" fill="#4ade8015" stroke="#4ade80" stroke-width="1"/> <text x="155" y="120" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#f8fafc">BIOSPHERE</text> <text x="155" y="135" text-anchor="middle" font-family="Arial, sans-serif" font-size="9" fill="#94a3b8">Life Forms</text> </g> <text x="25" y="240" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">Interactions:</text> <path d="M 40 260 L 220 260" stroke="#4ade80" stroke-width="1" opacity="0.4"/> <text x="25" y="280" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">• Volcanism affects Atmosphere</text> <text x="25" y="300" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">• Water shapes the Geosphere</text> <text x="25" y="320" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">• Life alters chemical cycles</text> <!-- Central ESS Graphic --> <circle cx="130" cy="365" r="20" fill="none" stroke="#4ade80" stroke-width="1" stroke-dasharray="2 2"/> <circle cx="130" cy="365" r="12" fill="#4ade80" fill-opacity="0.2"/> </g> <!-- Footer Banner --> <rect x="0" y="525" width="900" height="35" fill="#00000040"/> <text x="450" y="547" text-anchor="middle" font-family="Georgia, serif" font-style="italic" font-size="14" fill="#f59e0b">"The present is the key to the past." — Uniformitarianism</text> </svg>Introduction to Geology and the Scientific Method image 1Introduction to Geology and the Scientific Method - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/introduction-to-geology/svg/1Introduction to Geology and the Scientific Method diagram 1Introduction to Geology and the Scientific Method - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/introduction-to-geology/svg/2Introduction to Geology and the Scientific Method diagram 2Introduction to Geology and the Scientific Method - Geology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="60" text-anchor="middle" font-family="Arial, sans-serif" font-size="32" font-weight="bold" fill="#f8fafc" letter-spacing="1">MINERALS: THE BUILDING BLOCKS OF EARTH</text> <text x="450" y="85" text-anchor="middle" font-family="Arial, sans-serif" font-size="14" fill="#94a3b8" letter-spacing="2">A GEOLOGICAL OVERVIEW OF ATOMIC ARCHITECTURE</text> <line x1="300" y1="100" x2="600" y2="100" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 4"/> <!-- Left Panel: Chemical Bonding --> <rect x="40" y="130" width="260" height="390" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="165" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">I. CHEMICAL BONDING</text> <!-- Ionic --> <circle cx="75" cy="205" r="12" fill="#f59e0b" opacity="0.8"/> <circle cx="105" cy="205" r="15" fill="#38bdf8" opacity="0.8"/> <text x="130" y="202" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Ionic</text> <text x="130" y="216" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Electrostatic (Halite)</text> <!-- Covalent --> <circle cx="78" cy="265" r="14" fill="#e879f9" opacity="0.6"/> <circle cx="102" cy="265" r="14" fill="#e879f9" opacity="0.6"/> <text x="130" y="262" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Covalent</text> <text x="130" y="276" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Shared Electrons (Diamond)</text> <!-- Metallic --> <rect x="65" y="320" width="45" height="30" rx="4" fill="#94a3b8" opacity="0.3"/> <circle cx="75" cy="330" r="3" fill="#f8fafc"/> <circle cx="85" cy="340" r="3" fill="#f8fafc"/> <circle cx="95" cy="330" r="3" fill="#f8fafc"/> <text x="130" y="325" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Metallic</text> <text x="130" y="339" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Electron Sea (Gold)</text> <!-- Van der Waals --> <line x1="65" y1="385" x2="110" y2="385" stroke="#94a3b8" stroke-width="2"/> <line x1="65" y1="395" x2="110" y2="395" stroke="#94a3b8" stroke-width="2" stroke-dasharray="2 2"/> <line x1="65" y1="405" x2="110" y2="405" stroke="#94a3b8" stroke-width="2"/> <text x="130" y="392" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Van der Waals</text> <text x="130" y="406" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Weak Dipoles (Graphite)</text> <!-- Center Panel: Pauling's Rules --> <rect x="320" y="130" width="260" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="450" y="165" text-anchor="middle" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#f59e0b">II. RADIUS RATIO RULE</text> <!-- Formula --> <rect x="360" y="185" width="180" height="45" rx="8" fill="#00000030"/> <text x="450" y="213" text-anchor="middle" font-family="serif" font-size="20" fill="#f8fafc" font-style="italic">Rr = Rc / Ra</text> <!-- Coordination Graphic --> <circle cx="450" cy="300" r="35" fill="none" stroke="#38bdf8" stroke-width="1" stroke-dasharray="4 2"/> <circle cx="450" cy="300" r="8" fill="#f59e0b" filter="url(#glow)"/> <!-- Cation --> <circle cx="450" cy="265" r="12" fill="#38bdf8" opacity="0.6"/> <!-- Anions --> <circle cx="482" cy="315" r="12" fill="#38bdf8" opacity="0.6"/> <circle cx="418" cy="315" r="12" fill="#38bdf8" opacity="0.6"/> <text x="450" y="355" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Octahedral Coordination (CN=6)</text> <!-- Right Panel: Crystal Systems --> <rect x="600" y="130" width="260" height="390" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="620" y="165" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#e879f9">III. CRYSTAL SYSTEMS</text> <!-- Grid of Systems --> <!-- Cubic --> <rect x="625" y="190" width="30" height="30" fill="none" stroke="#f8fafc" stroke-width="1.5"/> <text x="670" y="202" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Cubic</text> <text x="670" y="215" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">a=b=c | 90°</text> <!-- Hexagonal --> <polygon points="640,250 655,258 655,275 640,283 625,275 625,258" fill="none" stroke="#f8fafc" stroke-width="1.5"/> <text x="670" y="262" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Hexagonal</text> <text x="670" y="275" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">a1=a2=a3≠c | 120°</text> <!-- Tetragonal --> <rect x="625" y="310" width="30" height="45" fill="none" stroke="#f8fafc" stroke-width="1.5"/> <text x="670" y="325" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Tetragonal</text> <text x="670" y="338" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">a=b≠c | 90°</text> <!-- Orthorhombic --> <rect x="625" y="380" width="40" height="25" fill="none" stroke="#f8fafc" stroke-width="1.5"/> <text x="680" y="392" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Orthorhombic</text> <text x="680" y="405" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">a≠b≠c | 90°</text> <!-- Monoclinic --> <polygon points="625,455 660,455 670,435 635,435" fill="none" stroke="#f8fafc" stroke-width="1.5"/> <text x="680" y="442" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Monoclinic</text> <text x="680" y="455" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">a≠b≠c | β≠90°</text> <!-- Bottom Process Bar --> <rect x="320" y="390" width="260" height="130" rx="16" fill="#38bdf815" stroke="#38bdf830"/> <text x="450" y="415" text-anchor="middle" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#38bdf8">STRUCTURAL HIERARCHY</text> <g transform="translate(345, 440)"> <circle cx="0" cy="0" r="5" fill="#f8fafc"/> <text x="0" y="20" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8">ATOM</text> <line x1="10" y1="0" x2="40" y2="0" stroke="#f8fafc" stroke-width="1"/> <circle cx="55" cy="0" r="8" fill="none" stroke="#f8fafc"/> <circle cx="55" cy="0" r="2" fill="#f8fafc"/> <text x="55" y="20" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8">UNIT CELL</text> <line x1="70" y1="0" x2="100" y2="0" stroke="#f8fafc" stroke-width="1"/> <rect x="110" y="-8" width="16" height="16" fill="none" stroke="#f8fafc"/> <text x="118" y="20" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8">LATTICE</text> <line x1="135" y1="0" x2="165" y2="0" stroke="#f8fafc" stroke-width="1"/> <path d="M 175,-10 L 195,-10 L 200,0 L 195,10 L 175,10 Z" fill="#f59e0b"/> <text x="188" y="25" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" font-weight="bold" fill="#f8fafc">MINERAL</text> </g> <!-- Decorative corner elements --> <path d="M 20 20 L 60 20 M 20 20 L 20 60" stroke="#38bdf8" stroke-width="2" fill="none" opacity="0.5"/> <path d="M 880 540 L 840 540 M 880 540 L 880 500" stroke="#e879f9" stroke-width="2" fill="none" opacity="0.5"/> </svg>Minerals: The Building Blocks of Earth image 1Minerals: The Building Blocks of Earth - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/minerals-and-gemology/svg/1Minerals: The Building Blocks of Earth diagram 1Minerals: The Building Blocks of Earth - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/minerals-and-gemology/svg/2Minerals: The Building Blocks of Earth diagram 2Minerals: The Building Blocks of Earth - Geology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="magmaGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#f59e0b"/> <stop offset="100%" stop-color="#ef4444"/> </linearGradient> <linearGradient id="spectrumGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#fecaca"/> <!-- Felsic --> <stop offset="33%" stop-color="#94a3b8"/> <!-- Intermediate --> <stop offset="66%" stop-color="#475569"/> <!-- Mafic --> <stop offset="100%" stop-color="#0f172a"/> <!-- Ultramafic --> </linearGradient> <pattern id="dots" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Subtle Grid Lines --> <path d="M 50 0 L 50 560 M 850 0 L 850 560" stroke="#ffffff05" stroke-width="1"/> <path d="M 0 80 L 900 80" stroke="#ffffff10" stroke-width="2"/> <!-- Header Section --> <text x="450" y="45" text-anchor="middle" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc">IGNEOUS PROCESSES &amp; VOLCANISM</text> <text x="450" y="68" text-anchor="middle" font-family="Arial, sans-serif" font-size="13" fill="#38bdf8" letter-spacing="3" font-weight="bold">THE THERMAL ENGINE OF CRUSTAL EVOLUTION</text> <!-- LEFT CARD: Magma Components --> <rect x="40" y="105" width="260" height="180" rx="16" fill="#ffffff10" stroke="#ffffff10"/> <text x="60" y="135" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">01. MAGMA ANATOMY</text> <text x="60" y="155" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">The parent material of all igneous rocks.</text> <circle cx="75" cy="185" r="12" fill="#ef4444" fill-opacity="0.8"/> <text x="95" y="182" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">MELT</text> <text x="95" y="195" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Mobile ions (Si, O, Al, Mg)</text> <rect x="63" y="210" width="24" height="24" rx="4" fill="#e879f9" fill-opacity="0.8"/> <text x="95" y="220" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">SOLIDS</text> <text x="95" y="233" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Crystallized silicate minerals</text> <path d="M 75 245 Q 85 255 75 265 Q 65 255 75 245" fill="#38bdf8" fill-opacity="0.8"/> <text x="95" y="255" font-family="Arial, sans-serif" font-weight="bold" font-size="14" fill="#f8fafc">VOLATILES</text> <text x="95" y="268" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Dissolved gases (H₂O, CO₂, SO₂)</text> <!-- CENTER CARD: Melting Triggers --> <rect x="320" y="105" width="260" height="180" rx="16" fill="#ffffff10" stroke="#ffffff10"/> <text x="340" y="135" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">02. MELTING TRIGGERS</text> <!-- Icon: Decompression --> <path d="M 340 170 L 360 150 L 380 170" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="390" y="165" font-family="Arial, sans-serif" font-weight="bold" font-size="13" fill="#f8fafc">DECOMPRESSION</text> <text x="390" y="178" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Pressure drop (Mid-ocean ridges)</text> <!-- Icon: Flux --> <circle cx="360" cy="205" r="8" fill="none" stroke="#38bdf8" stroke-width="2"/> <path d="M 360 197 L 360 213 M 352 205 L 368 205" stroke="#38bdf8" stroke-width="2"/> <text x="390" y="205" font-family="Arial, sans-serif" font-weight="bold" font-size="13" fill="#f8fafc">FLUX MELTING</text> <text x="390" y="218" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Volatile addition (Subduction)</text> <!-- Icon: Heat --> <circle cx="360" cy="245" r="10" fill="url(#magmaGrad)"/> <text x="390" y="245" font-family="Arial, sans-serif" font-weight="bold" font-size="13" fill="#f8fafc">HEAT TRANSFER</text> <text x="390" y="258" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">Rising plumes (Hotspots)</text> <!-- RIGHT CARD: Petrology --> <rect x="600" y="105" width="260" height="180" rx="16" fill="#ffffff10" stroke="#ffffff10"/> <text x="620" y="135" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">03. PETROLOGY</text> <rect x="620" y="155" width="100" height="40" rx="8" fill="#ffffff05" stroke="#ffffff20"/> <text x="670" y="175" text-anchor="middle" font-family="Arial, sans-serif" font-weight="bold" font-size="12" fill="#f8fafc">INTRUSIVE</text> <text x="670" y="188" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8">Slow Cooling / Large Crystals</text> <rect x="730" y="155" width="100" height="40" rx="8" fill="#ffffff05" stroke="#ffffff20"/> <text x="780" y="175" text-anchor="middle" font-family="Arial, sans-serif" font-weight="bold" font-size="12" fill="#f8fafc">EXTRUSIVE</text> <text x="780" y="188" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8">Fast Cooling / Fine Grained</text> <text x="620" y="220" font-family="Arial, sans-serif" font-weight="bold" font-size="12" fill="#e879f9">TEXTURES:</text> <text x="620" y="240" font-family="Arial, sans-serif" font-size="11" fill="#f8fafc">• Phaneritic (Visible)</text> <text x="620" y="255" font-family="Arial, sans-serif" font-size="11" fill="#f8fafc">• Aphanitic (Microscopic)</text> <text x="740" y="240" font-family="Arial, sans-serif" font-size="11" fill="#f8fafc">• Porphyritic</text> <text x="740" y="255" font-family="Arial, sans-serif" font-size="11" fill="#f8fafc">• Vitreous</text> <!-- BOTTOM CARD: Compositional Spectrum --> <rect x="40" y="305" width="820" height="220" rx="16" fill="#ffffff10" stroke="#ffffff10"/> <text x="60" y="335" font-family="Arial, sans-serif" font-weight="bold" font-size="20" fill="#f59e0b">THE COMPOSITIONAL SPECTRUM</text> <!-- Spectrum Bar --> <rect x="60" y="360" width="780" height="40" rx="20" fill="url(#spectrumGrad)"/> <!-- Spectrum Labels --> <g font-family="Arial, sans-serif" font-weight="bold" font-size="14"> <text x="157" y="420" text-anchor="middle" fill="#fecaca">FELSIC</text> <text x="352" y="420" text-anchor="middle" fill="#94a3b8">INTERMEDIATE</text> <text x="547" y="420" text-anchor="middle" fill="#64748b">MAFIC</text> <text x="742" y="420" text-anchor="middle" fill="#475569">ULTRAMAFIC</text> </g> <!-- Data Table Overlay --> <g font-family="Arial, sans-serif" font-size="11" fill="#f8fafc"> <text x="60" y="450" fill="#94a3b8" font-weight="bold">SILICA (SiO₂)</text> <text x="157" y="450" text-anchor="middle">&gt; 65%</text> <text x="352" y="450" text-anchor="middle">55 – 65%</text> <text x="547" y="450" text-anchor="middle">45 – 55%</text> <text x="742" y="450" text-anchor="middle">&lt; 45%</text> <text x="60" y="475" fill="#94a3b8" font-weight="bold">TEMP (°C)</text> <text x="157" y="475" text-anchor="middle">600 – 800</text> <text x="352" y="475" text-anchor="middle">800 – 1000</text> <text x="547" y="475" text-anchor="middle">1000 – 1200</text> <text x="742" y="475" text-anchor="middle">&gt; 1200</text> <text x="60" y="500" fill="#94a3b8" font-weight="bold">ROCK TYPE</text> <text x="157" y="500" text-anchor="middle">Rhyolite / Granite</text> <text x="352" y="500" text-anchor="middle">Andesite / Diorite</text> <text x="547" y="500" text-anchor="middle">Basalt / Gabbro</text> <text x="742" y="500" text-anchor="middle">Komatiite / Peridotite</text> </g> <!-- Bowen's Reaction Series Indicator --> <path d="M 60 535 L 840 535" stroke="#ffffff20" stroke-width="1" stroke-dasharray="4"/> <text x="450" y="550" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8" letter-spacing="1">BOWEN'S REACTION SERIES: CRYSTALLIZATION SEQUENCE FROM RIGHT (HIGH T) TO LEFT (LOW T)</text> <!-- Decorative Accents --> <circle cx="860" cy="40" r="20" fill="#f59e0b" fill-opacity="0.1"/> <circle cx="860" cy="40" r="10" fill="#f59e0b" fill-opacity="0.2"/> <path d="M 30 30 L 50 30 M 40 20 L 40 40" stroke="#38bdf8" stroke-width="2" opacity="0.5"/> </svg>Igneous Processes and Volcanism image 1Igneous Processes and Volcanism - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/igneous-rocks-and-volcanism/svg/1Igneous Processes and Volcanism diagram 1Igneous Processes and Volcanism - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/igneous-rocks-and-volcanism/svg/2Igneous Processes and Volcanism diagram 2Igneous Processes and Volcanism - Geology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Definitions for Gradients and Styles --> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <linearGradient id="soilGrad" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#4ade80" stop-opacity="0.2"/> <stop offset="100%" stop-color="#f59e0b" stop-opacity="0.1"/> </linearGradient> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="bold" fill="#f8fafc" letter-spacing="1">THE EARTH'S SURFACE ARCHIVE</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">Weathering, Pedogenesis, and the Sedimentary Cycle</text> <rect x="350" y="85" width="200" height="2" fill="url(#accentGrad)" rx="1"/> <!-- Left Column: Weathering Engines --> <rect x="30" y="110" width="260" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="45" y="140" font-family="sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">1. WEATHERING ENGINES</text> <!-- Mechanical Sub-section --> <g transform="translate(45, 160)"> <rect width="230" height="75" rx="8" fill="#ffffff05"/> <text x="10" y="20" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f59e0b">MECHANICAL (Physical)</text> <text x="10" y="38" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Frost Wedging (Ice expansion)</text> <text x="10" y="53" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Exfoliation (Pressure release)</text> <text x="10" y="68" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Thermal Expansion (Arid heat)</text> <!-- Icon: Cracked Rock --> <path d="M180 20 L210 20 L220 50 L170 50 Z" fill="none" stroke="#f59e0b" stroke-width="1.5"/> <path d="M195 20 L190 35 L200 50" fill="none" stroke="#f59e0b" stroke-width="1.5"/> </g> <!-- Chemical Sub-section --> <g transform="translate(45, 245)"> <rect width="230" height="75" rx="8" fill="#ffffff05"/> <text x="10" y="20" font-family="sans-serif" font-size="13" font-weight="bold" fill="#e879f9">CHEMICAL (Decomposition)</text> <text x="10" y="38" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Oxidation (Rusting / Fe2O3)</text> <text x="10" y="53" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Hydrolysis (Silicate to Clay)</text> <text x="10" y="68" font-family="sans-serif" font-size="11" fill="#cbd5e1">• Carbonation (Acid dissolution)</text> <!-- Icon: Beaker --> <path d="M190 25 L190 55 A5 5 0 0 0 200 55 L200 25" fill="none" stroke="#e879f9" stroke-width="1.5"/> <circle cx="195" cy="45" r="2" fill="#e879f9"/> <circle cx="192" cy="38" r="1.5" fill="#e879f9"/> </g> <!-- Surface Area Logic --> <g transform="translate(45, 330)"> <text x="0" y="20" font-family="sans-serif" font-size="12" font-weight="bold" fill="#94a3b8">SURFACE AREA EFFECT</text> <rect x="0" y="30" width="30" height="30" fill="#38bdf833" stroke="#38bdf8"/> <text x="40" y="48" font-family="sans-serif" font-size="18" fill="#f8fafc">→</text> <g transform="translate(70, 30)"> <rect x="0" y="0" width="14" height="14" fill="#38bdf833" stroke="#38bdf8"/> <rect x="16" y="0" width="14" height="14" fill="#38bdf833" stroke="#38bdf8"/> <rect x="0" y="16" width="14" height="14" fill="#38bdf833" stroke="#38bdf8"/> <rect x="16" y="16" width="14" height="14" fill="#38bdf833" stroke="#38bdf8"/> </g> <text x="110" y="48" font-family="sans-serif" font-size="10" fill="#94a3b8">Fragmentation increases reaction sites</text> </g> <!-- Middle Column: Goldich Dissolution Series --> <rect x="310" y="110" width="280" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="325" y="140" font-family="sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">2. GOLDICH SERIES</text> <text x="325" y="160" font-family="sans-serif" font-size="11" fill="#94a3b8">Mineral Stability at Surface Conditions</text> <!-- Stability Scale --> <g transform="translate(340, 180)"> <defs> <linearGradient id="stabilityGrad" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#fb7185"/> <stop offset="100%" stop-color="#38bdf8"/> </linearGradient> </defs> <rect x="0" y="0" width="12" height="220" rx="6" fill="url(#stabilityGrad)"/> <!-- Labels --> <g font-family="sans-serif" font-size="11" font-weight="bold"> <text x="25" y="15" fill="#fb7185">OLIVINE (Least Stable)</text> <text x="25" y="55" fill="#f8fafc">Pyroxene</text> <text x="25" y="95" fill="#f8fafc">Amphibole</text> <text x="25" y="135" fill="#f8fafc">Biotite / Feldspar</text> <text x="25" y="175" fill="#f8fafc">Muscovite</text> <text x="25" y="215" fill="#38bdf8">QUARTZ (Most Stable)</text> </g> <!-- Arrow heads --> <path d="M-5 10 L6 -5 L17 10" fill="none" stroke="#fb7185" stroke-width="2"/> <path d="M-5 210 L6 225 L17 210" fill="none" stroke="#38bdf8" stroke-width="2"/> </g> <!-- Right Column: Pedogenesis (Soil) --> <rect x="610" y="110" width="260" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="625" y="140" font-family="sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">3. SOIL HORIZONS</text> <!-- Soil Profile --> <g transform="translate(625, 160)"> <!-- O --> <rect x="0" y="0" width="60" height="15" fill="#1a2e05" stroke="#ffffff20"/> <text x="70" y="12" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">O: Organic</text> <!-- A --> <rect x="0" y="15" width="60" height="30" fill="#422006" stroke="#ffffff20"/> <text x="70" y="35" font-family="sans-serif" font-size="12" fill="#cbd5e1">A: Topsoil</text> <!-- E --> <rect x="0" y="45" width="60" height="25" fill="#94a3b8" stroke="#ffffff20"/> <text x="70" y="62" font-family="sans-serif" font-size="12" fill="#cbd5e1">E: Eluviated</text> <!-- B --> <rect x="0" y="70" width="60" height="45" fill="#92400e" stroke="#ffffff20"/> <text x="70" y="97" font-family="sans-serif" font-size="12" fill="#cbd5e1">B: Subsoil</text> <!-- C --> <rect x="0" y="115" width="60" height="40" fill="#78350f" stroke="#ffffff20" fill-opacity="0.6"/> <text x="70" y="140" font-family="sans-serif" font-size="12" fill="#cbd5e1">C: Regolith</text> <!-- R --> <rect x="0" y="155" width="60" height="40" fill="#334155" stroke="#ffffff20"/> <text x="70" y="180" font-family="sans-serif" font-size="12" fill="#cbd5e1">R: Bedrock</text> <!-- Grass on top --> <path d="M2 0 L5 -8 M10 0 L12 -6 M20 0 L18 -10 M30 0 L32 -7 M45 0 L43 -9 M55 0 L58 -6" stroke="#4ade80" stroke-width="1.5"/> </g> <!-- CLORPT Equation --> <g transform="translate(625, 375)"> <text x="0" y="0" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f59e0b">CLORPT EQUATION</text> <text x="0" y="25" font-family="sans-serif" font-size="16" fill="#f8fafc">S = f(Cl, O, R, P, T)</text> <text x="0" y="45" font-family="sans-serif" font-size="10" fill="#94a3b8">Climate, Organisms, Relief, Parent, Time</text> </g> <!-- Footer / Process Flow --> <rect x="30" y="450" width="840" height="80" rx="16" fill="#ffffff10" stroke="#ffffff20"/> <g transform="translate(60, 495)"> <circle cx="0" cy="0" r="15" fill="#38bdf8"/> <text x="0" y="5" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#0f172a">1</text> <text x="25" y="5" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">WEATHERING</text> <line x1="130" y1="0" x2="180" y2="0" stroke="#94a3b8" stroke-dasharray="4"/> <circle cx="210" cy="0" r="15" fill="#38bdf8"/> <text x="210" y="5" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#0f172a">2</text> <text x="235" y="5" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">EROSION</text> <line x1="310" y1="0" x2="360" y2="0" stroke="#94a3b8" stroke-dasharray="4"/> <circle cx="390" cy="0" r="15" fill="#38bdf8"/> <text x="390" y="5" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#0f172a">3</text> <text x="415" y="5" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">TRANSPORT</text> <line x1="510" y1="0" x2="560" y2="0" stroke="#94a3b8" stroke-dasharray="4"/> <circle cx="590" cy="0" r="15" fill="#38bdf8"/> <text x="590" y="5" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#0f172a">4</text> <text x="615" y="5" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">DEPOSITION</text> <line x1="710" y1="0" x2="740" y2="0" stroke="#94a3b8" stroke-dasharray="4"/> <text x="755" y="5" font-family="sans-serif" font-size="14" font-weight="bold" fill="#e879f9">LITHIFICATION</text> </g> <!-- Decorative corner elements --> <path d="M880 20 L880 50 M850 20 L880 20" fill="none" stroke="#38bdf8" stroke-width="2"/> <path d="M20 540 L20 510 M20 540 L50 540" fill="none" stroke="#38bdf8" stroke-width="2"/> </svg>Weathering, Sediments, and Sedimentary Rocks image 1Weathering, Sediments, and Sedimentary Rocks - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/weathering-and-sedimentary-rocks/svg/1Weathering, Sediments, and Sedimentary Rocks diagram 1Weathering, Sediments, and Sedimentary Rocks - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/weathering-and-sedimentary-rocks/svg/2Weathering, Sediments, and Sedimentary Rocks diagram 2Weathering, Sediments, and Sedimentary Rocks - Geology - diagram 2https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/weathering-and-sedimentary-rocks/svg/3Weathering, Sediments, and Sedimentary Rocks diagram 3Weathering, Sediments, and Sedimentary Rocks - Geology - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg-grad" x1="0%" y1="0%" x2="0%" y2="100%"> <stop offset="0%" style="stop-color:#0f172a;stop-opacity:1" /> <stop offset="100%" style="stop-color:#1e1b4b;stop-opacity:1" /> </linearGradient> <linearGradient id="card-grad" x1="0%" y1="0%" x2="100%" y2="100%"> <stop offset="0%" style="stop-color:#ffffff15;stop-opacity:1" /> <stop offset="100%" style="stop-color:#ffffff05;stop-opacity:1" /> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg-grad)" /> <rect width="900" height="560" fill="url(#grid)" /> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="32" letter-spacing="1">METAMORPHISM &amp; THE ROCK CYCLE</text> <text x="450" y="75" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="400" letter-spacing="2">A THERMODYNAMIC NETWORK OF CRUSTAL TRANSFORMATION</text> <line x1="350" y1="85" x2="550" y2="85" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2" /> <!-- Main Central Network --> <!-- Igneous Node --> <rect x="360" y="120" width="180" height="70" rx="12" fill="url(#card-grad)" stroke="#f43f5e" stroke-width="2" /> <text x="450" y="150" text-anchor="middle" fill="#f43f5e" font-family="sans-serif" font-weight="700" font-size="18">IGNEOUS</text> <text x="450" y="170" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="11">Crystallized Magma</text> <!-- Sedimentary Node --> <rect x="120" y="320" width="180" height="70" rx="12" fill="url(#card-grad)" stroke="#fbbf24" stroke-width="2" /> <text x="210" y="350" text-anchor="middle" fill="#fbbf24" font-family="sans-serif" font-weight="700" font-size="18">SEDIMENTARY</text> <text x="210" y="370" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="11">Lithified Sediments</text> <!-- Metamorphic Node --> <rect x="600" y="320" width="180" height="70" rx="12" fill="url(#card-grad)" stroke="#a855f7" stroke-width="2" filter="url(#glow)" /> <text x="690" y="350" text-anchor="middle" fill="#a855f7" font-family="sans-serif" font-weight="700" font-size="18">METAMORPHIC</text> <text x="690" y="370" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="11">Recrystallized Solid State</text> <!-- Transition Paths (Arrows) --> <path d="M 450 190 Q 450 355 600 355" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="5,5" marker-end="url(#arrow)" /> <path d="M 300 355 L 600 355" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="5,5" /> <path d="M 210 320 Q 210 155 360 155" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="5,5" /> <!-- Labels on Paths --> <rect x="410" y="250" width="80" height="20" rx="10" fill="#0f172a" /> <text x="450" y="264" text-anchor="middle" fill="#38bdf8" font-family="sans-serif" font-size="10" font-weight="bold">HEAT + PRESSURE</text> <rect x="360" y="345" width="80" height="20" rx="10" fill="#0f172a" /> <text x="400" y="359" text-anchor="middle" fill="#38bdf8" font-family="sans-serif" font-size="10" font-weight="bold">BURIAL</text> <!-- Left Sidebar: Drivers --> <rect x="30" y="120" width="220" height="160" rx="16" fill="#ffffff10" /> <text x="45" y="145" fill="#f59e0b" font-family="sans-serif" font-weight="700" font-size="16">DRIVERS OF CHANGE</text> <!-- Driver 1: Heat --> <circle cx="55" cy="175" r="8" fill="#f43f5e" /> <text x="75" y="179" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">Temperature (T)</text> <text x="75" y="192" fill="#94a3b8" font-family="sans-serif" font-size="10">Activation energy for reactions.</text> <!-- Driver 2: Pressure --> <rect x="47" y="210" width="16" height="16" rx="2" fill="#38bdf8" /> <text x="75" y="222" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">Pressure (P)</text> <text x="75" y="235" fill="#94a3b8" font-family="sans-serif" font-size="10">Lithostatic &amp; Differential stress.</text> <!-- Driver 3: Fluids --> <path d="M 55 250 Q 63 265 55 265 Q 47 265 55 250" fill="#10b981" /> <text x="75" y="262" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">Fluids (X)</text> <text x="75" y="275" fill="#94a3b8" font-family="sans-serif" font-size="10">Catalysts for ion migration.</text> <!-- Right Sidebar: The Rule --> <rect x="650" y="120" width="220" height="160" rx="16" fill="#ffffff10" /> <text x="665" y="145" fill="#e879f9" font-family="sans-serif" font-weight="700" font-size="16">THE SOLID STATE RULE</text> <text x="665" y="170" fill="#f8fafc" font-family="sans-serif" font-size="12" font-style="italic">"Metamorphism does not"</text> <text x="665" y="185" fill="#f8fafc" font-family="sans-serif" font-size="12" font-style="italic">"involve melting."</text> <line x1="665" y1="205" x2="850" y2="205" stroke="#ffffff20" stroke-width="1" /> <text x="665" y="225" fill="#94a3b8" font-family="sans-serif" font-size="11">If melting occurs → Anatexis</text> <text x="665" y="240" fill="#94a3b8" font-family="sans-serif" font-size="11">Result → Igneous Realm</text> <text x="665" y="265" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">P = ρ · g · h</text> <!-- Bottom Quote Panel --> <rect x="150" y="450" width="600" height="70" rx="35" fill="#ffffff08" stroke="#38bdf8" stroke-width="1" stroke-opacity="0.3" /> <text x="450" y="480" text-anchor="middle" fill="#f8fafc" font-family="serif" font-style="italic" font-size="15">"The Earth is a heat engine, and the rock cycle is the physical manifestation"</text> <text x="450" y="500" text-anchor="middle" fill="#f8fafc" font-family="serif" font-style="italic" font-size="15">"of the planet's attempt to reach thermodynamic equilibrium."</text> <!-- Decorative Elements --> <circle cx="850" cy="50" r="30" fill="#f59e0b" fill-opacity="0.1" /> <circle cx="850" cy="50" r="15" fill="#f59e0b" fill-opacity="0.2" /> <circle cx="50" cy="510" r="20" fill="#38bdf8" fill-opacity="0.1" /> <!-- Markov Chain Dots (Subtle) --> <g opacity="0.4"> <circle cx="450" cy="220" r="3" fill="#f8fafc" /> <circle cx="470" cy="230" r="3" fill="#f8fafc" /> <circle cx="430" cy="230" r="3" fill="#f8fafc" /> <path d="M 430 230 L 450 220 L 470 230" stroke="#f8fafc" stroke-width="0.5" fill="none" /> </g> </svg>Metamorphism and the Rock Cycle image 1Metamorphism and the Rock Cycle - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/metamorphism-and-rock-cycle/svg/1Metamorphism and the Rock Cycle diagram 1Metamorphism and the Rock Cycle - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/metamorphism-and-rock-cycle/svg/2Metamorphism and the Rock Cycle diagram 2Metamorphism and the Rock Cycle - Geology - diagram 2https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/geologic-time-and-history/svg/1Measuring Geologic Time and Earth History diagram 1Measuring Geologic Time and Earth History - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/geologic-time-and-history/svg/2Measuring Geologic Time and Earth History diagram 2Measuring Geologic Time and Earth History - Geology - diagram 2https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/geologic-time-and-history/svg/3Measuring Geologic Time and Earth History diagram 3Measuring Geologic Time and Earth History - Geology - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="coreGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#fbbf24"/> <stop offset="100%" stop-color="#f59e0b"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background and Grid --> <rect width="900" height="560" fill="url(#bg)"/> <g stroke="#ffffff08" stroke-width="1"> <line x1="0" y1="100" x2="900" y2="100"/> <line x1="0" y1="200" x2="900" y2="200"/> <line x1="0" y1="300" x2="900" y2="300"/> <line x1="0" y1="400" x2="900" y2="400"/> <line x1="0" y1="500" x2="900" y2="500"/> <line x1="100" y1="0" x2="100" y2="560"/> <line x1="300" y1="0" x2="300" y2="560"/> <line x1="500" y1="0" x2="500" y2="560"/> <line x1="700" y1="0" x2="700" y2="560"/> </g> <!-- Header --> <text x="40" y="55" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="-1">EARTH'S INTERIOR &amp; TECTONICS</text> <text x="40" y="80" font-family="sans-serif" font-size="14" font-weight="400" fill="#94a3b8" text-transform="uppercase" letter-spacing="2">The Grand Unified Theory of Geology</text> <rect x="40" y="95" width="820" height="2" fill="#38bdf8" fill-opacity="0.3"/> <!-- Main Earth Slice Panel --> <rect x="40" y="120" width="440" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="150" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">I. STRATIFIED STRUCTURE</text> <!-- Earth Slice Illustration --> <g transform="translate(420, 340)"> <!-- Inner Core --> <circle r="40" fill="url(#coreGrad)" filter="url(#glow)"/> <!-- Outer Core --> <path d="M -80 0 A 80 80 0 0 1 80 0" fill="none" stroke="#f97316" stroke-width="30" stroke-opacity="0.6"/> <!-- Mantle --> <path d="M -150 0 A 150 150 0 0 1 150 0" fill="none" stroke="#ea580c" stroke-width="80" stroke-opacity="0.4"/> <!-- Crust --> <path d="M -195 0 A 195 195 0 0 1 195 0" fill="none" stroke="#38bdf8" stroke-width="8"/> <!-- Labels for Slice --> <g font-family="sans-serif" font-size="11" font-weight="600"> <text x="0" y="5" text-anchor="middle" fill="#0f172a">INNER CORE</text> <text x="0" y="-65" text-anchor="middle" fill="#f8fafc">OUTER CORE (LIQUID)</text> <text x="0" y="-130" text-anchor="middle" fill="#f8fafc">MANTLE (SOLID/DUCTILE)</text> <text x="0" y="-205" text-anchor="middle" fill="#38bdf8">LITHOSPHERE (RIGID)</text> </g> </g> <!-- Compositional vs Rheological Legend --> <g transform="translate(60, 410)" font-family="sans-serif"> <text y="0" font-size="13" font-weight="700" fill="#f8fafc">COMPOSITIONAL</text> <text y="18" font-size="11" fill="#94a3b8">Crust (Silicates) • Mantle (Peridotite) • Core (Fe-Ni)</text> <text y="50" font-size="13" font-weight="700" fill="#f8fafc">RHEOLOGICAL</text> <text y="68" font-size="11" fill="#94a3b8">Lithosphere (Brittle) • Asthenosphere (Plastic)</text> </g> <!-- Isostasy Panel --> <rect x="500" y="120" width="360" height="190" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="520" y="150" font-family="sans-serif" font-size="18" font-weight="700" fill="#f59e0b">II. ISOSTASY</text> <!-- Isostasy Diagram --> <g transform="translate(520, 170)"> <rect x="0" y="60" width="320" height="40" fill="#ea580c" fill-opacity="0.2"/> <!-- Mantle --> <text x="5" y="90" font-family="sans-serif" font-size="10" fill="#ea580c">ASTHENOSPHERE (DENSE)</text> <!-- Oceanic Crust --> <rect x="20" y="55" width="80" height="10" fill="#38bdf8" rx="2"/> <text x="20" y="50" font-family="sans-serif" font-size="10" fill="#38bdf8">OCEANIC</text> <!-- Continental Crust + Root --> <path d="M 140 60 L 280 60 L 280 100 L 210 115 L 140 100 Z" fill="#94a3b8" fill-opacity="0.8"/> <rect x="140" y="30" width="140" height="30" fill="#94a3b8"/> <text x="145" y="25" font-family="sans-serif" font-size="10" fill="#f8fafc">CONTINENTAL (MTN)</text> <path d="M 210 65 L 210 110" stroke="#f59e0b" stroke-width="1" stroke-dasharray="2,2"/> <text x="215" y="95" font-family="sans-serif" font-size="10" fill="#f59e0b">ROOT (r)</text> </g> <!-- Convection Panel --> <rect x="500" y="330" width="360" height="190" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="520" y="360" font-family="sans-serif" font-size="18" font-weight="700" fill="#e879f9">III. THE ENGINE</text> <!-- Convection Diagram --> <g transform="translate(680, 440)"> <!-- Heat Source --> <circle r="15" fill="#f97316" filter="url(#glow)"/> <text x="0" y="5" text-anchor="middle" font-family="sans-serif" font-size="8" font-weight="bold" fill="#f8fafc">HEAT</text> <!-- Convection Loops --> <g fill="none" stroke-width="3" stroke-linecap="round"> <!-- Left Loop --> <path d="M -25 -10 Q -60 -60 -100 -10 Q -60 40 -25 10" stroke="#f97316" stroke-opacity="0.6"> <animate attributeName="stroke-dashoffset" from="100" to="0" dur="3s" repeatCount="indefinite" /> </path> <!-- Right Loop --> <path d="M 25 -10 Q 60 -60 100 -10 Q 60 40 25 10" stroke="#f97316" stroke-opacity="0.6"/> </g> <text x="0" y="-65" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="600" fill="#f8fafc">MANTLE CONVECTION</text> <text x="0" y="-50" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">Driving Plate Motion</text> <!-- Arrows --> <path d="M -80 -40 L -100 -50 L -120 -40" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="-100" y="-60" text-anchor="middle" font-family="sans-serif" font-size="9" fill="#38bdf8">SLAB PULL</text> </g> <!-- Footer Info --> <text x="860" y="540" text-anchor="end" font-family="sans-serif" font-size="10" fill="#475569">GEOLOGY SERIES • VOL 01 • PLATE TECTONICS</text> </svg>Earth's Interior and Plate Tectonics image 1Earth's Interior and Plate Tectonics - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/plate-tectonics-and-interior/svg/1Earth's Interior and Plate Tectonics diagram 1Earth's Interior and Plate Tectonics - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/plate-tectonics-and-interior/svg/2Earth's Interior and Plate Tectonics diagram 2Earth's Interior and Plate Tectonics - Geology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#f59e0b"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-1">EARTHQUAKES &amp; GEOLOGICAL STRUCTURES</text> <text x="40" y="85" font-family="sans-serif" font-size="16" fill="#94a3b8" font-weight="400">The Mechanics of Crustal Deformation and Seismic Failure</text> <rect x="40" y="105" width="120" height="4" rx="2" fill="url(#accentGrad)"/> <!-- Left Column: The Physics of Failure --> <rect x="40" y="130" width="260" height="390" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="165" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">MECHANICS</text> <!-- Stress/Strain --> <g transform="translate(60, 190)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <text x="11" y="21" font-family="serif" font-style="italic" font-size="16" fill="#38bdf8">σ</text> <text x="45" y="12" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Stress</text> <text x="45" y="28" font-family="sans-serif" font-size="11" fill="#94a3b8">Force applied per unit area.</text> </g> <g transform="translate(60, 240)"> <circle cx="15" cy="15" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="1.5"/> <text x="11" y="21" font-family="serif" font-style="italic" font-size="16" fill="#e879f9">ε</text> <text x="45" y="12" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Strain</text> <text x="45" y="28" font-family="sans-serif" font-size="11" fill="#94a3b8">Resulting physical change.</text> </g> <!-- Mohr's Circle Mini-Graphic --> <g transform="translate(60, 310)"> <path d="M 0 60 L 180 60 M 20 0 L 20 70" stroke="#94a3b8" stroke-width="1"/> <circle cx="90" cy="60" r="30" fill="none" stroke="#38bdf8" stroke-width="2"/> <line x1="20" y1="50" x2="180" y2="10" stroke="#f43f5e" stroke-dasharray="4"/> <text x="125" y="15" font-family="sans-serif" font-size="9" fill="#f43f5e">FAILURE ENVELOPE</text> <text x="10" y="85" font-family="sans-serif" font-size="10" fill="#94a3b8" font-weight="600">MOHR-COULOMB CRITERION</text> </g> <!-- Middle Section: Deformation Stages --> <text x="330" y="155" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">DEFORMATION STAGES</text> <g transform="translate(330, 175)"> <!-- Stage 1 --> <rect width="530" height="60" rx="12" fill="#ffffff08"/> <circle cx="30" cy="30" r="15" fill="#10b981" /> <text x="26" y="35" font-family="sans-serif" font-weight="bold" font-size="14" fill="#fff">1</text> <text x="60" y="25" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Elastic Deformation</text> <text x="60" y="42" font-family="sans-serif" font-size="12" fill="#94a3b8">Temporary bending. Stores energy like a spring. Reversible.</text> <!-- Stage 2 --> <rect y="75" width="530" height="60" rx="12" fill="#ffffff08"/> <circle cx="30" cy="105" r="15" fill="#f59e0b" /> <text x="26" y="110" font-family="sans-serif" font-weight="bold" font-size="14" fill="#fff">2</text> <text x="60" y="100" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Ductile (Plastic) Flow</text> <text x="60" y="117" font-family="sans-serif" font-size="12" fill="#94a3b8">Permanent bending. Occurs at depth (high T/P). Forms Folds.</text> <!-- Stage 3 --> <rect y="150" width="530" height="60" rx="12" fill="#ffffff08"/> <circle cx="30" cy="180" r="15" fill="#f43f5e" /> <text x="26" y="185" font-family="sans-serif" font-weight="bold" font-size="14" fill="#fff">3</text> <text x="60" y="175" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Brittle Failure</text> <text x="60" y="192" font-family="sans-serif" font-size="12" fill="#94a3b8">Fracturing and displacement. Occurs near surface. Forms Faults.</text> </g> <!-- Bottom Section: Tectonic Regimes --> <g transform="translate(330, 410)"> <text y="-10" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">TECTONIC ENVIRONMENTS</text> <!-- Compression --> <g transform="translate(0, 10)"> <rect width="165" height="100" rx="12" fill="#f59e0b15" stroke="#f59e0b40"/> <text x="15" y="25" font-family="sans-serif" font-weight="bold" font-size="13" fill="#f59e0b">COMPRESSION</text> <path d="M 40 55 L 20 55 M 30 45 L 40 55 L 30 65" stroke="#f59e0b" fill="none" stroke-width="2"/> <path d="M 125 55 L 145 55 M 135 45 L 125 55 L 135 65" stroke="#f59e0b" fill="none" stroke-width="2"/> <text x="15" y="75" font-family="sans-serif" font-size="11" fill="#f8fafc">Convergent Boundary</text> <text x="15" y="88" font-family="sans-serif" font-size="11" fill="#94a3b8" font-weight="600">Folds / Reverse Faults</text> </g> <!-- Tension --> <g transform="translate(182, 10)"> <rect width="165" height="100" rx="12" fill="#38bdf815" stroke="#38bdf840"/> <text x="15" y="25" font-family="sans-serif" font-weight="bold" font-size="13" fill="#38bdf8">TENSION</text> <path d="M 20 55 L 40 55 M 30 45 L 20 55 L 30 65" stroke="#38bdf8" fill="none" stroke-width="2"/> <path d="M 145 55 L 125 55 M 135 45 L 145 55 L 135 65" stroke="#38bdf8" fill="none" stroke-width="2"/> <text x="15" y="75" font-family="sans-serif" font-size="11" fill="#f8fafc">Divergent Boundary</text> <text x="15" y="88" font-family="sans-serif" font-size="11" fill="#94a3b8" font-weight="600">Normal Faults</text> </g> <!-- Shear --> <g transform="translate(365, 10)"> <rect width="165" height="100" rx="12" fill="#e879f915" stroke="#e879f940"/> <text x="15" y="25" font-family="sans-serif" font-weight="bold" font-size="13" fill="#e879f9">SHEAR</text> <path d="M 40 45 L 125 45 M 115 35 L 125 45 L 115 55" stroke="#e879f9" fill="none" stroke-width="2"/> <path d="M 125 65 L 40 65 M 50 55 L 40 65 L 50 75" stroke="#e879f9" fill="none" stroke-width="2"/> <text x="15" y="75" font-family="sans-serif" font-size="11" fill="#f8fafc">Transform Boundary</text> <text x="15" y="88" font-family="sans-serif" font-size="11" fill="#94a3b8" font-weight="600">Strike-Slip Faults</text> </g> </g> <!-- Decorative Element --> <path d="M 800 50 Q 850 100 800 150 T 800 250" fill="none" stroke="url(#accentGrad)" stroke-width="2" opacity="0.3"/> <circle cx="850" cy="480" r="60" fill="#ffffff05" stroke="#ffffff10"/> <circle cx="850" cy="480" r="40" fill="#ffffff05" stroke="#ffffff10"/> </svg>Earthquakes and Geological Structures image 1Earthquakes and Geological Structures - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/earthquakes-and-structures/svg/1Earthquakes and Geological Structures diagram 1Earthquakes and Geological Structures - Geology - diagram 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stroke="#ffffff08" stroke-width="1"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="40" y="50" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">HYDROLOGY</text> <text x="245" y="50" font-family="sans-serif" font-weight="300" font-size="32" fill="#38bdf8">THE DYNAMICS OF WATER</text> <rect x="40" y="65" width="120" height="4" fill="#f59e0b" rx="2"/> <text x="40" y="85" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">STREAMS • FLOODS • GROUNDWATER</text> <!-- Left Panel: Surface Systems --> <rect x="40" y="110" width="400" height="280" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="60" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">SURFACE DYNAMICS</text> <!-- Stream Profile Graphic --> <path d="M 70 280 Q 150 280, 200 220 T 380 180" fill="none" stroke="#38bdf8" stroke-width="3" stroke-dasharray="4 2"/> <circle cx="75" cy="180" r="4" fill="#f59e0b"/> <text x="85" y="185" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">HEADWATERS</text> <text x="85" y="200" font-family="sans-serif" font-size="11" fill="#94a3b8">Erosional Dominance (V-Valleys)</text> <circle cx="210" cy="230" r="4" fill="#f59e0b"/> <text x="220" y="235" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">TRUNK STREAM</text> <text x="220" y="250" font-family="sans-serif" font-size="11" fill="#94a3b8">Transport Dominance (Meandering)</text> <circle cx="340" cy="280" r="4" fill="#f59e0b"/> <text x="240" y="310" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc" text-anchor="end">MOUTH / DELTA</text> <text x="240" y="325" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="end">Depositional Dominance</text> <!-- Manning's Snippet --> <rect x="60" y="340" width="360" height="35" rx="8" fill="#00000040"/> <text x="75" y="362" font-family="monospace" font-size="12" fill="#e879f9">v = (1/n) * R^(2/3) * S^(1/2)</text> <text x="310" y="362" font-family="sans-serif" font-size="10" fill="#94a3b8">MANNING'S EQUATION</text> <!-- Right Panel: Groundwater --> <rect x="460" y="110" width="400" height="280" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="480" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">THE HIDDEN RESERVOIR</text> <!-- Porosity/Permeability Visual --> <g transform="translate(480, 160)"> <!-- Porous Material --> <rect width="180" height="100" rx="8" fill="#1e293b" stroke="#38bdf820"/> <text x="10" y="-10" font-family="sans-serif" font-size="12" fill="#38bdf8">HIGH POROSITY</text> <circle cx="30" cy="30" r="12" fill="#94a3b830" stroke="#94a3b8"/> <circle cx="60" cy="30" r="12" fill="#94a3b830" stroke="#94a3b8"/> <circle cx="90" cy="30" r="12" fill="#94a3b830" stroke="#94a3b8"/> <circle cx="30" cy="70" r="12" 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<text x="465" y="485" font-family="sans-serif" font-size="12" fill="#f8fafc">Groundwater represents 98% of Earth's liquid freshwater.</text> <text x="465" y="502" font-family="sans-serif" font-size="12" fill="#f8fafc">It moves through pores and fractures, not underground rivers.</text> <!-- Decorative elements --> <circle cx="850" cy="50" r="20" fill="none" stroke="#38bdf8" stroke-width="1" stroke-opacity="0.3"/> <circle cx="850" cy="50" r="12" fill="none" stroke="#f59e0b" stroke-width="1" stroke-opacity="0.3"/> <path d="M 840 50 H 860 M 850 40 V 60" stroke="#f8fafc" stroke-width="1" stroke-opacity="0.5"/> </svg>Hydrology: Streams, Floods, and Groundwater image 1Hydrology: Streams, Floods, and Groundwater - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/hydrology-streams-and-groundwater/svg/1Hydrology: Streams, Floods, and Groundwater diagram 1Hydrology: Streams, Floods, and Groundwater - Geology - diagram 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in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <!-- Decorative Grid --> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="32" letter-spacing="2">EARTH IN MOTION</text> <text x="450" y="75" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="400">MECHANICS OF MASS WASTING &amp; GLACIATION</text> <rect x="400" y="85" width="100" height="3" fill="#f59e0b" rx="1.5"/> <!-- Left Panel: Mass Wasting --> <rect x="40" y="110" width="400" height="280" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="60" y="145" fill="#f59e0b" font-family="sans-serif" font-weight="700" font-size="20">MASS WASTING</text> <text x="60" y="165" fill="#94a3b8" font-family="sans-serif" font-size="12">Gravity-driven transport of lithospheric material.</text> <!-- Slope Diagram --> <path d="M 80 340 L 320 340 L 320 200 Z" fill="#334155" stroke="#475569" stroke-width="2"/> <path d="M 120 340 L 320 220" stroke="#f59e0b" stroke-width="3" stroke-dasharray="4 2" opacity="0.6"/> <circle cx="220" cy="280" r="25" fill="#475569" stroke="#f8fafc" stroke-width="2"/> <!-- Forces --> <path d="M 220 280 L 220 320" stroke="#f8fafc" stroke-width="2" marker-end="url(#arrow)"/> <!-- Gravity --> <path d="M 220 280 L 260 255" stroke="#e879f9" stroke-width="2"/> <!-- Shear --> <text x="230" y="325" fill="#f8fafc" font-family="sans-serif" font-size="10">G</text> <text x="265" y="250" fill="#e879f9" font-family="sans-serif" font-size="10">Shear Stress</text> <!-- Right Panel: Glaciation --> <rect x="460" y="110" width="400" height="280" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="480" y="145" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="20">GLACIATION</text> <text x="480" y="165" fill="#94a3b8" font-family="sans-serif" font-size="12">Plastic flow of crystalline H₂O under pressure.</text> <!-- Glacier Diagram --> <path d="M 500 220 Q 650 200 820 340 L 500 340 Z" fill="#0ea5e9" opacity="0.3"/> <path d="M 500 220 Q 650 200 820 340" stroke="#38bdf8" stroke-width="3" fill="none"/> <!-- Flow Arrows --> <path d="M 550 250 Q 600 260 650 280" stroke="#f8fafc" stroke-width="2" fill="none" opacity="0.8"/> <path d="M 560 280 Q 610 290 660 310" stroke="#f8fafc" stroke-width="2" fill="none" opacity="0.8"/> <circle cx="750" cy="320" r="15" fill="#f8fafc20" stroke="#38bdf8" stroke-dasharray="2 1"/> <text x="710" y="355" fill="#38bdf8" font-family="sans-serif" font-size="10" font-weight="bold">PLASTIC DEFORMATION</text> <!-- Bottom Panel: Physics --> <rect x="40" y="410" width="820" height="120" rx="16" fill="#ffffff08" stroke="#ffffff10" stroke-width="1"/> <!-- Formula Section --> <text x="70" y="445" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="16">THE FACTOR OF SAFETY (Fs)</text> <rect x="70" y="460" width="280" height="50" rx="8" fill="#00000030"/> <text x="85" y="492" fill="#f8fafc" font-family="serif" font-style="italic" font-size="22">Fs = Σ Resisting / Σ Driving</text> <!-- Status Indicators --> <g transform="translate(400, 440)"> <circle cx="20" cy="20" r="12" fill="#22c55e" opacity="0.2"/> <circle cx="20" cy="20" r="5" fill="#22c55e"/> <text x="45" y="25" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="bold">Fs &gt; 1.0 : STABLE</text> <circle cx="20" cy="55" r="12" fill="#ef4444" opacity="0.2"/> <circle cx="20" cy="55" r="5" fill="#ef4444"/> <text x="45" y="60" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="bold">Fs ≤ 1.0 : FAILURE</text> </g> <!-- Parameters --> <g transform="translate(620, 435)"> <text x="0" y="15" fill="#94a3b8" font-family="sans-serif" font-size="11" font-weight="bold">KEY VARIABLES</text> <text x="0" y="35" fill="#f8fafc" font-family="sans-serif" font-size="12">• Slope Angle (α)</text> <text x="0" y="55" fill="#f8fafc" font-family="sans-serif" font-size="12">• Pore Pressure (u)</text> <text x="0" y="75" fill="#f8fafc" font-family="sans-serif" font-size="12">• Cohesion (c)</text> <text x="130" y="35" fill="#f8fafc" font-family="sans-serif" font-size="12">• Friction (φ)</text> <text x="130" y="55" fill="#f8fafc" font-family="sans-serif" font-size="12">• Vegetation</text> <text x="130" y="75" fill="#f8fafc" font-family="sans-serif" font-size="12">• Seismicity</text> </g> <!-- Markers --> <defs> <marker id="arrow" markerWidth="10" markerHeight="10" refX="9" refY="3" orient="auto" markerUnits="strokeWidth"> <path d="M0,0 L0,6 L9,3 z" fill="#f8fafc" /> </marker> </defs> </svg>Mass Wasting and Glaciation image 1Mass Wasting and Glaciation - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/mass-wasting-and-glaciation/svg/1Mass Wasting and Glaciation diagram 1Mass Wasting and Glaciation - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/mass-wasting-and-glaciation/svg/2Mass Wasting and Glaciation diagram 2Mass Wasting and Glaciation - Geology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="oceanGrad" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#38bdf8" stop-opacity="0.2"/> <stop offset="100%" stop-color="#38bdf8" stop-opacity="0.05"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> 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fill="#94a3b8" text-anchor="middle">SURFACE SUBMERGED</text> <!-- Comparison Panels --> <!-- Active Margin --> <rect x="40" y="110" width="400" height="160" rx="16" fill="#ffffff08" stroke="#e879f933"/> <circle cx="70" cy="140" r="12" fill="#e879f9"/> <path d="M65 140l10 0M70 135l0 10" stroke="white" stroke-width="2"/> <text x="95" y="145" font-family="sans-serif" font-weight="bold" font-size="18" fill="#f8fafc">ACTIVE MARGINS</text> <text x="70" y="175" font-family="sans-serif" font-size="13" fill="#cbd5e1">• High Tectonic Activity (Subduction)</text> <text x="70" y="195" font-family="sans-serif" font-size="13" fill="#cbd5e1">• Narrow Continental Shelves</text> <text x="70" y="215" font-family="sans-serif" font-size="13" fill="#cbd5e1">• Deep-Ocean Trenches present</text> <text x="70" y="245" font-family="sans-serif" font-weight="bold" font-size="11" fill="#e879f9" letter-spacing="1">EXAMPLE: WEST COAST, SOUTH AMERICA</text> <!-- Passive Margin --> <rect x="460" y="110" width="400" height="160" rx="16" fill="#ffffff08" stroke="#38bdf833"/> <circle cx="490" cy="140" r="12" fill="#38bdf8"/> <path d="M485 140l10 0" stroke="white" stroke-width="2"/> <text x="515" y="145" font-family="sans-serif" font-weight="bold" font-size="18" fill="#f8fafc">PASSIVE MARGINS</text> <text x="490" y="175" font-family="sans-serif" font-size="13" fill="#cbd5e1">• Minimal Activity (Intraplate)</text> <text x="490" y="195" font-family="sans-serif" font-size="13" fill="#cbd5e1">• Broad Continental Shelves</text> <text x="490" y="215" font-family="sans-serif" font-size="13" fill="#cbd5e1">• Thick Sedimentary Clastic Wedges</text> <text x="490" y="245" font-family="sans-serif" font-weight="bold" font-size="11" fill="#38bdf8" letter-spacing="1">EXAMPLE: EAST COAST, USA</text> <!-- Main Illustration Area --> <rect x="40" y="290" width="820" height="240" rx="16" fill="#00000020"/> <!-- Ocean Floor Profile --> <path d="M40 350 L120 355 L180 420 L220 480 L250 470 L300 475 L450 475 L500 430 L530 460 L560 410 L600 475 L750 475 L800 530 L830 400 L860 350" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <path d="M40 350 L120 355 L180 420 L220 480 L250 470 L300 475 L450 475 L500 430 L530 460 L560 410 L600 475 L750 475 L800 530 L830 400 L860 350 V530 H40 Z" fill="url(#oceanGrad)"/> <!-- Annotations for Diagram --> <g font-family="sans-serif" font-size="11" font-weight="bold"> <!-- Passive Side --> <text x="80" y="340" fill="#94a3b8" text-anchor="middle">SHELF</text> <line x1="120" y1="355" x2="120" y2="330" stroke="#94a3b8" stroke-dasharray="2,2"/> <text x="160" y="390" fill="#94a3b8" transform="rotate(35 160 390)">SLOPE</text> <text x="230" y="505" fill="#38bdf8" text-anchor="middle">CONTINENTAL RISE</text> <path d="M230 495 l0 -15" stroke="#38bdf8" stroke-width="1"/> <!-- Abyssal Plain --> <text x="375" y="505" fill="#f8fafc" text-anchor="middle">ABYSSAL PLAIN</text> <text x="375" y="520" fill="#94a3b8" text-anchor="middle" font-weight="normal" font-size="9">PELAGIC SEDIMENT SINK</text> <!-- Mid-Ocean Ridge --> <text x="530" y="390" fill="#f59e0b" text-anchor="middle">MID-OCEAN RIDGE</text> <path d="M530 400 l0 20" stroke="#f59e0b" stroke-width="1"/> <text x="530" y="375" fill="#94a3b8" text-anchor="middle" font-weight="normal" font-size="9">SEAFLOOR SPREADING</text> <!-- Active Side --> <text x="815" y="550" fill="#e879f9" text-anchor="middle">TRENCH</text> <path d="M815 535 l0 -15" stroke="#e879f9" stroke-width="1"/> <text x="815" y="340" fill="#94a3b8" text-anchor="middle">ACTIVE MARGIN</text> </g> <!-- Depth Scale --> <g stroke="#94a3b8" stroke-width="1" opacity="0.5"> <line x1="55" y1="350" x2="65" y2="350"/> <line x1="55" y1="410" x2="65" y2="410"/> <line x1="55" y1="475" x2="65" y2="475"/> <line x1="55" y1="530" x2="65" y2="530"/> </g> <g font-family="sans-serif" font-size="9" fill="#94a3b8"> <text x="70" y="353">0m</text> <text x="70" y="413">2,000m</text> <text x="70" y="478">5,000m</text> <text x="70" y="533">11,000m</text> </g> <!-- Crust Composition Labels --> <rect x="280" y="305" width="340" height="35" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <text x="300" y="327" font-family="sans-serif" font-size="12" fill="#f8fafc"> <tspan font-weight="bold" fill="#f59e0b">CRUST:</tspan> <tspan fill="#cbd5e1" dx="10">Continental (Granitic / Thick)</tspan> <tspan fill="#38bdf8" dx="20">Oceanic (Basaltic / Thin)</tspan> </text> <!-- Decorative Elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#ffffff05" stroke-width="8"/> <circle cx="850" cy="50" r="15" fill="none" stroke="#ffffff05" stroke-width="4"/> </svg>Geology of the Oceans and Shorelines image 1Geology of the Oceans and Shorelines - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/oceans-and-shorelines/svg/1Geology of the Oceans and Shorelines diagram 1Geology of the Oceans and Shorelines - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/oceans-and-shorelines/svg/2Geology of the Oceans and Shorelines diagram 2Geology of the Oceans and Shorelines - Geology - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff08" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background and Texture --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Subtle Grid Lines --> <g stroke="#ffffff0a" stroke-width="1"> <line x1="0" y1="100" x2="900" y2="100" /> <line x1="0" y1="200" x2="900" y2="200" /> <line x1="0" y1="300" x2="900" y2="300" /> <line x1="0" y1="400" x2="900" y2="400" /> <line x1="0" y1="500" x2="900" y2="500" /> </g> <!-- Header Section --> <text x="40" y="55" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-0.5">CLIMATE CHANGE &amp; ENVIRONMENTAL GEOLOGY</text> <text x="40" y="80" font-family="sans-serif" font-weight="400" font-size="14" fill="#94a3b8" text-transform="uppercase" letter-spacing="2">Earth System Science (ESS) &amp; Radiative Dynamics</text> <rect x="40" y="95" width="120" height="4" rx="2" fill="#f59e0b" /> <!-- Column 1: The Earth System (Spheres) --> <rect x="40" y="120" width="260" height="410" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="60" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">THE EARTH SYSTEM</text> <!-- Sphere: Atmosphere --> <g transform="translate(60, 170)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <path d="M8 12 Q15 8 22 12 M8 18 Q15 14 22 18" stroke="#38bdf8" fill="none" stroke-linecap="round"/> <text x="40" y="12" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Atmosphere</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Heat transport &amp; insulation</text> </g> <!-- Sphere: Hydrosphere --> <g transform="translate(60, 225)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <path d="M8 18 Q11 12 15 18 T22 18" stroke="#38bdf8" fill="none" stroke-linecap="round"/> <text x="40" y="12" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Hydrosphere</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Thermal inertia &amp; CO2 sink</text> </g> <!-- Sphere: Cryosphere --> <g transform="translate(60, 280)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <path d="M15 8 L15 22 M8 15 L22 15 M10 10 L20 20 M10 20 L20 10" stroke="#38bdf8" fill="none" stroke-linecap="round"/> <text x="40" y="12" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Cryosphere</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Albedo &amp; sea-level storage</text> </g> <!-- Sphere: Geosphere --> <g transform="translate(60, 335)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <path d="M8 22 L15 8 L22 22 Z" stroke="#38bdf8" fill="none" stroke-linecap="round"/> <text x="40" y="12" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Geosphere</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Long-term carbon storage</text> </g> <!-- Sphere: Biosphere --> <g transform="translate(60, 390)"> <circle cx="15" cy="15" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <path d="M15 22 C15 22 22 15 22 10 C22 5 15 5 15 5 C15 5 8 5 8 10 C8 15 15 22 15 22" stroke="#38bdf8" fill="none" stroke-linecap="round"/> <text x="40" y="12" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Biosphere</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Rapid carbon cycling</text> </g> <!-- Column 2: Radiative Balance (Greenhouse Effect) --> <rect x="320" y="120" width="260" height="410" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="340" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">RADIATIVE BALANCE</text> <!-- Greenhouse Diagram --> <g transform="translate(340, 180)"> <!-- Sun --> <circle cx="30" cy="30" r="15" fill="#f59e0b" filter="glow"/> <g stroke="#f59e0b" stroke-width="2"> <line x1="30" y1="5" x2="30" y2="10"/> <line x1="30" y1="50" x2="30" y2="55"/> <line x1="5" y1="30" x2="10" y2="30"/> <line x1="50" y1="30" x2="55" y2="30"/> </g> <!-- Earth Surface --> <path d="M20 180 Q110 160 200 180" stroke="#94a3b8" stroke-width="4" fill="none"/> <path d="M20 150 Q110 130 200 150" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 4" fill="none" opacity="0.5"/> <text x="100" y="145" font-family="sans-serif" font-size="10" fill="#38bdf8" text-anchor="middle">Atmosphere Layer</text> <!-- Incoming Solar --> <path d="M45 45 L100 165" stroke="#f59e0b" stroke-width="3" marker-end="url(#arrow-gold)"/> <text x="55" y="100" font-family="sans-serif" font-size="10" fill="#f59e0b" transform="rotate(65 55 100)">Shortwave (UV/Vis)</text> <!-- Outgoing Terrestrial --> <path d="M110 165 L130 145 Q150 120 130 100" stroke="#e879f9" stroke-width="3" fill="none"/> <path d="M130 145 L160 165" stroke="#e879f9" stroke-width="3" fill="none"/> <text x="140" y="90" font-family="sans-serif" font-size="10" fill="#e879f9">Longwave (IR) Trapped</text> </g> <!-- Stefan-Boltzmann Formula --> <rect x="340" y="400" width="220" height="100" rx="8" fill="#00000030"/> <text x="355" y="425" font-family="serif" font-style="italic" font-size="16" fill="#f8fafc">P = σ A T⁴</text> <text x="355" y="445" font-family="sans-serif" font-size="11" fill="#94a3b8">σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴</text> <text x="355" y="465" font-family="sans-serif" font-size="11" fill="#f8fafc">Natural GHE: +33°C</text> <text x="355" y="480" font-family="sans-serif" font-size="10" fill="#94a3b8">Keeps Earth habitable (15°C avg)</text> <!-- Column 3: Feedback & Proxies --> <rect x="600" y="120" width="260" height="410" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="620" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">FEEDBACK LOOPS</text> <!-- Positive Feedback --> <g transform="translate(620, 170)"> <rect width="220" height="70" rx="8" fill="#f43f5e15" stroke="#f43f5e" stroke-width="1"/> <text x="10" y="20" font-family="sans-serif" font-weight="700" font-size="12" fill="#f43f5e">POSITIVE (Amplifying)</text> <text x="10" y="40" font-family="sans-serif" font-size="11" fill="#f8fafc">Ice-Albedo: Temp ↑ → Ice ↓</text> <text x="10" y="55" font-family="sans-serif" font-size="11" fill="#f8fafc">→ Albedo ↓ → Absorption ↑</text> <path d="M190 20 L210 20 L210 50 L190 50" stroke="#f43f5e" fill="none" stroke-width="2"/> <path d="M190 50 L195 45 M190 50 L195 55" stroke="#f43f5e" fill="none" stroke-width="2"/> </g> <!-- Negative Feedback --> <g transform="translate(620, 255)"> <rect width="220" height="70" rx="8" fill="#10b98115" stroke="#10b981" stroke-width="1"/> <text x="10" y="20" font-family="sans-serif" font-weight="700" font-size="12" fill="#10b981">NEGATIVE (Stabilizing)</text> <text x="10" y="40" font-family="sans-serif" font-size="11" fill="#f8fafc">CO2 Greening: CO2 ↑ → Plant ↑</text> <text x="10" y="55" font-family="sans-serif" font-size="11" fill="#f8fafc">→ Photosynthesis ↑ → CO2 ↓</text> <path d="M210 20 L190 20 L190 50 L210 50" stroke="#10b981" fill="none" stroke-width="2"/> <path d="M210 50 L205 45 M210 50 L205 55" stroke="#10b981" fill="none" stroke-width="2"/> </g> <!-- Paleoclimate Proxies --> <text x="620" y="360" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">GEOLOGIC PROXIES</text> <g transform="translate(620, 380)"> <rect width="220" height="120" rx="8" fill="#ffffff05" stroke="#ffffff10" stroke-width="1"/> <text x="10" y="25" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">δ¹⁸O Isotope Ratios</text> <text x="10" y="45" font-family="sans-serif" font-size="11" fill="#94a3b8">Heavy oxygen (¹⁸O) enrichment</text> <text x="10" y="60" font-family="sans-serif" font-size="11" fill="#94a3b8">in oceans indicates glacial growth.</text> <line x1="10" y1="80" x2="210" y2="80" stroke="#ffffff20" stroke-width="1"/> <text x="10" y="100" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">Ice Cores</text> <text x="10" y="112" font-family="sans-serif" font-size="11" fill="#94a3b8">Trapped gas bubbles (CO2, CH4)</text> </g> <!-- Markers --> <defs> <marker id="arrow-gold" markerWidth="10" markerHeight="10" refX="9" refY="3" orient="auto" markerUnits="strokeWidth"> <path d="M0,0 L0,6 L9,3 z" fill="#f59e0b" /> </marker> </defs> </svg>Climate Change and Environmental Geology image 1Climate Change and Environmental Geology - Geology - image 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/climate-change-and-environmental-geology/svg/1Climate Change and Environmental Geology diagram 1Climate Change and Environmental Geology - Geology - diagram 1https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/climate-change-and-environmental-geology/svg/2Climate Change and Environmental Geology diagram 2Climate Change and Environmental Geology - Geology - diagram 2https://www.getlykke.com/explore/public/geology-6ae93dc4-518d-4048-acd3-523e6d6aff20/media/climate-change-and-environmental-geology/svg/3Climate Change and Environmental Geology diagram 3Climate Change and Environmental Geology - Geology - diagram 3https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb90492026-04-20T05:00:44.000Zhttps://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/limits-and-continuity/svg/1Limits and Continuity diagram 1Limits and Continuity - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/limits-and-continuity/svg/2Limits and Continuity diagram 2Limits and Continuity - AP/College Calculus BC - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Background and Definitions --> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff08" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Base Layers --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Subtle Grid Lines --> <g stroke="#ffffff05" stroke-width="1"> <line x1="0" y1="280" x2="900" y2="280" /> <line x1="450" y1="0" x2="450" y2="560" /> </g> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="1">DIFFERENTIATION: FUNDAMENTALS</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="400" fill="#94a3b8" letter-spacing="2">THE MATHEMATICAL STUDY OF INSTANTANEOUS CHANGE</text> <rect x="400" y="95" width="100" height="3" fill="#38bdf8" rx="1.5"/> <!-- Left Column: Physics Chain --> <rect x="30" y="120" width="220" height="410" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="50" y="150" font-family="sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">PHYSICS OF MOTION</text> <g transform="translate(50, 180)"> <!-- Position --> <circle cx="20" cy="20" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <text x="17" y="25" fill="#38bdf8" font-family="serif" font-weight="bold">s</text> <text x="50" y="18" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Position</text> <text x="50" y="34" font-family="sans-serif" font-size="11" fill="#94a3b8">Location over time f(t)</text> <!-- Arrow --> <path d="M20 45 L20 75" stroke="#94a3b8" stroke-width="2" marker-end="url(#arrowhead)" stroke-dasharray="4 2"/> <!-- Velocity --> <g transform="translate(0, 80)"> <circle cx="20" cy="20" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="17" y="25" fill="#e879f9" font-family="serif" font-weight="bold">v</text> <text x="50" y="18" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Velocity</text> <text x="50" y="34" font-family="sans-serif" font-size="11" fill="#94a3b8">Rate of change s'(t)</text> </g> <!-- Arrow --> <path d="M20 125 L20 155" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4 2"/> <!-- Acceleration --> <g transform="translate(0, 160)"> <circle cx="20" cy="20" r="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2"/> <text x="17" y="25" fill="#f59e0b" font-family="serif" font-weight="bold">a</text> <text x="50" y="18" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Acceleration</text> <text x="50" y="34" font-family="sans-serif" font-size="11" fill="#94a3b8">Rate of change v'(t)</text> </g> </g> <text x="50" y="480" font-family="sans-serif" font-size="12" fill="#94a3b8" font-style="italic">"The derivative of position</text> <text x="50" y="496" font-family="sans-serif" font-size="12" fill="#94a3b8" font-style="italic">is velocity; the derivative of</text> <text x="50" y="512" font-family="sans-serif" font-size="12" fill="#94a3b8" font-style="italic">velocity is acceleration."</text> <!-- Center Column: The Limit Definition --> <rect x="270" y="120" width="360" height="260" rx="16" fill="#ffffff12" stroke="#ffffff20"/> <text x="450" y="150" text-anchor="middle" font-family="sans-serif" font-size="18" font-weight="bold" fill="#f59e0b">THE FORMAL DEFINITION</text> <!-- Graph Visualization --> <g transform="translate(320, 170)"> <!-- Axes --> <line x1="0" y1="100" x2="180" y2="100" stroke="#94a3b8" stroke-width="1"/> <line x1="20" y1="120" x2="20" y2="10" stroke="#94a3b8" stroke-width="1"/> <!-- Curve --> <path d="M30 90 Q 80 85, 160 20" stroke="#38bdf8" stroke-width="3" fill="none"/> <!-- Tangent Line --> <line x1="50" y1="95" x2="170" y2="15" stroke="#f59e0b" stroke-width="2" filter="url(#glow)"/> <!-- Points --> <circle cx="107" cy="58" r="4" fill="#f8fafc"/> <text x="115" y="65" font-family="serif" font-size="12" fill="#f8fafc">P</text> <!-- Zoom Circle Label --> <circle cx="107" cy="58" r="25" stroke="#ffffff30" stroke-width="1" fill="none" stroke-dasharray="2 2"/> <text x="140" y="85" font-family="sans-serif" font-size="10" fill="#94a3b8">Slope at a point</text> </g> <!-- Formula Box --> <rect x="300" y="295" width="300" height="60" rx="8" fill="#00000040"/> <text x="450" y="330" text-anchor="middle" font-family="serif" font-size="18" fill="#f8fafc"> f'(x) = lim <tspan baseline-shift="sub" font-size="10">h→0</tspan> [ f(x+h) - f(x) ] / h </text> <!-- Right Column: The Rules --> <rect x="650" y="120" width="220" height="410" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="670" y="150" font-family="sans-serif" font-size="18" font-weight="bold" fill="#e879f9">THE TOOLKIT</text> <g transform="translate(670, 180)"> <!-- Power Rule --> <rect width="180" height="80" rx="8" fill="#ffffff05" stroke="#e879f930"/> <text x="10" y="25" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Power Rule</text> <text x="10" y="55" font-family="serif" font-size="16" fill="#38bdf8">d/dx [xⁿ] = nxⁿ⁻¹</text> <!-- Product Rule --> <g transform="translate(0, 100)"> <rect width="180" height="80" rx="8" fill="#ffffff05" stroke="#e879f930"/> <text x="10" y="25" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Product Rule</text> <text x="10" y="55" font-family="serif" font-size="15" fill="#38bdf8">(uv)' = u'v + uv'</text> </g> <!-- Quotient Rule --> <g transform="translate(0, 200)"> <rect width="180" height="80" rx="8" fill="#ffffff05" stroke="#e879f930"/> <text x="10" y="25" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Chain Rule</text> <text x="10" y="55" font-family="serif" font-size="15" fill="#38bdf8">dy/dx = dy/du · du/dx</text> </g> </g> <!-- Bottom Center: Differentiability --> <rect x="270" y="400" width="360" height="130" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="290" y="430" font-family="sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">Differentiability vs. Continuity</text> <g transform="translate(290, 450)"> <!-- Smooth Curve --> <path d="M10 40 Q 30 10, 50 40 T 90 40" stroke="#38bdf8" stroke-width="2" fill="none"/> <text x="10" y="65" font-family="sans-serif" font-size="10" fill="#94a3b8">Smooth (Diff.)</text> <!-- Cusp --> <path d="M120 40 L 145 10 L 170 40" stroke="#f43f5e" stroke-width="2" fill="none"/> <text x="120" y="65" font-family="sans-serif" font-size="10" fill="#94a3b8">Sharp Turn (Not Diff.)</text> <!-- Vertical --> <path d="M220 50 C 240 50, 240 0, 260 0" stroke="#f43f5e" stroke-width="2" fill="none"/> <text x="210" y="65" font-family="sans-serif" font-size="10" fill="#94a3b8">Vertical (Not Diff.)</text> </g> <text x="450" y="515" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#94a3b8" font-style="italic">Differentiability implies continuity, but continuity does not imply differentiability.</text> <!-- Decorative Accents --> <circle cx="850" cy="50" r="40" fill="#38bdf808" stroke="#38bdf810" stroke-width="1"/> <circle cx="850" cy="50" r="25" fill="#38bdf808" stroke="#38bdf810" stroke-width="1"/> <path d="M30 30 L 60 30 M 30 30 L 30 60" stroke="#f59e0b" stroke-width="2" opacity="0.5"/> </svg>Differentiation: Fundamentals image 1Differentiation: Fundamentals - AP/College Calculus BC - image 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/differentiation-fundamentals/svg/1Differentiation: Fundamentals diagram 1Differentiation: Fundamentals - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/differentiation-fundamentals/svg/2Differentiation: Fundamentals diagram 2Differentiation: Fundamentals - AP/College Calculus BC - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bgGradient" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bgGradient)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">ADVANCED DIFFERENTIATION</text> <text x="40" y="85" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">DECONSTRUCTING THE MACHINERY OF CHANGE</text> <line x1="40" y1="105" x2="860" y2="105" stroke="#334155" stroke-width="1"/> <!-- Left Column: THE CHAIN RULE --> <rect x="40" y="130" width="400" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="75" cy="165" r="15" fill="#f59e0b" fill-opacity="0.2"/> <path d="M 70 165 L 80 165 M 75 160 L 75 170" stroke="#f59e0b" stroke-width="2" fill="none"/> <text x="100" y="170" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">THE CHAIN RULE</text> <text x="65" y="205" font-family="serif" font-style="italic" font-size="22" fill="#f8fafc">dy/dx = (dy/du) · (du/dx)</text> <text x="65" y="235" font-family="sans-serif" font-size="13" fill="#cbd5e1">The "Inside-Outside" engine for composite functions.</text> <!-- Visual Representation of Chain Rule (Nested Circles) --> <circle cx="100" cy="300" r="30" fill="none" stroke="#f59e0b" stroke-width="2" stroke-dasharray="4 2"/> <circle cx="100" cy="300" r="15" fill="#f59e0b" fill-opacity="0.4"/> <path d="M 140 300 L 170 300" stroke="#94a3b8" stroke-width="1" marker-end="url(#arrowhead)"/> <rect x="200" y="270" width="210" height="80" rx="8" fill="#00000030"/> <text x="210" y="290" font-family="monospace" font-size="11" fill="#38bdf8"># Neural Network Context</text> <text x="210" y="310" font-family="monospace" font-size="11" fill="#94a3b8">def backprop(error, weight):</text> <text x="210" y="330" font-family="monospace" font-size="11" fill="#94a3b8"> return error * weight.grad</text> <!-- Right Column: IMPLICIT DIFFERENTIATION --> <rect x="460" y="130" width="400" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="495" cy="165" r="15" fill="#38bdf8" fill-opacity="0.2"/> <path d="M 490 160 Q 495 175 500 160" stroke="#38bdf8" stroke-width="2" fill="none"/> <text x="520" y="170" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">IMPLICIT RELATIONS</text> <text x="485" y="205" font-family="serif" font-style="italic" font-size="22" fill="#f8fafc">x² + y² = r² → y' = -x/y</text> <text x="485" y="235" font-family="sans-serif" font-size="13" fill="#cbd5e1">Differentiating intertwined variables where y = f(x) is hidden.</text> <!-- Visual Representation: Implicit Circle --> <circle cx="540" cy="305" r="35" fill="none" stroke="#334155" stroke-width="1"/> <line x1="500" y1="270" x2="580" y2="340" stroke="#38bdf8" stroke-width="2" filter="url(#glow)"/> <text x="590" y="295" font-family="sans-serif" font-size="11" fill="#94a3b8">Tangent at (x,y)</text> <text x="590" y="315" font-family="sans-serif" font-size="11" fill="#94a3b8">requires dy/dx isolation</text> <!-- Bottom Section: HIGHER ORDER DERIVATIVES --> <rect x="40" y="390" width="820" height="130" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="100" y="425" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">HIGHER-ORDER LAYERS</text> <!-- Step 1 --> <rect x="70" y="445" width="230" height="50" rx="8" fill="#e879f910" stroke="#e879f930"/> <text x="85" y="465" font-family="sans-serif" font-weight="bold" font-size="12" fill="#e879f9">f'(x)</text> <text x="85" y="482" font-family="sans-serif" font-size="11" fill="#94a3b8">VELOCITY / SLOPE</text> <!-- Arrow --> <path d="M 310 470 L 340 470" stroke="#475569" stroke-width="2" fill="none"/> <!-- Step 2 --> <rect x="350" y="445" width="230" height="50" rx="8" fill="#e879f920" stroke="#e879f950"/> <text x="365" y="465" font-family="sans-serif" font-weight="bold" font-size="12" fill="#e879f9">f''(x)</text> <text x="365" y="482" font-family="sans-serif" font-size="11" fill="#94a3b8">ACCELERATION / CONCAVITY</text> <!-- Arrow --> <path d="M 590 470 L 620 470" stroke="#475569" stroke-width="2" fill="none"/> <!-- Step 3 --> <rect x="630" y="445" width="190" height="50" rx="8" fill="#e879f930" stroke="#e879f9"/> <text x="645" y="465" font-family="sans-serif" font-weight="bold" font-size="12" fill="#f8fafc">f'''(x)</text> <text x="645" y="482" font-family="sans-serif" font-size="11" fill="#f8fafc">JERK / RATE OF CURVATURE</text> <!-- Footer Decor --> <text x="860" y="540" font-family="monospace" font-size="10" fill="#334155" text-anchor="end">CALCULUS_SERIES_VOL_04 // ADV_DIFF_TECHNIQUES</text> <!-- Abstract Shapes --> <circle cx="830" cy="60" r="20" fill="none" stroke="#334155" stroke-width="1"/> <circle cx="830" cy="60" r="10" fill="#e879f9" fill-opacity="0.3"/> <rect x="780" y="50" width="15" height="15" fill="none" stroke="#334155" stroke-width="1" transform="rotate(45 787.5 57.5)"/> </svg>Advanced Differentiation Techniques image 1Advanced Differentiation Techniques - AP/College Calculus BC - image 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/advanced-differentiation/svg/1Advanced Differentiation Techniques diagram 1Advanced Differentiation Techniques - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/advanced-differentiation/svg/2Advanced Differentiation Techniques diagram 2Advanced Differentiation Techniques - AP/College Calculus BC - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/contextual-applications-differentiation/svg/1Contextual Applications of Differentiation diagram 1Contextual Applications of Differentiation - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/contextual-applications-differentiation/svg/2Contextual Applications of Differentiation diagram 2Contextual Applications of Differentiation - AP/College Calculus BC - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/contextual-applications-differentiation/svg/3Contextual Applications of Differentiation diagram 3Contextual Applications of Differentiation - AP/College Calculus BC - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Definitions: Gradients, Filters, and Patterns --> <defs> <linearGradient id="bg-grad" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dot-pattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff08"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> <linearGradient id="accent-amber" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#f59e0b"/> <stop offset="100%" stop-color="#d97706"/> </linearGradient> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg-grad)"/> <rect width="900" height="560" fill="url(#dot-pattern)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">ANALYTICAL APPLICATIONS OF DIFFERENTIATION</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">Bridging Pure Calculation and Applied Reality</text> <line x1="300" y1="90" x2="600" y2="90" stroke="#334155" stroke-width="1"/> <!-- Left Panel: EVT --> <rect x="40" y="110" width="390" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">I. Extreme Value Theorem (EVT)</text> <text x="60" y="160" font-family="sans-serif" font-size="12" fill="#94a3b8">Guarantees existence of Absolute Extrema on [a, b].</text> <!-- EVT Mini-Graph --> <path d="M 80 300 Q 150 180 220 250 T 380 220" fill="none" stroke="#475569" stroke-width="2" stroke-dasharray="4"/> <path d="M 100 300 Q 150 180 220 250 T 340 235" fill="none" stroke="#f59e0b" stroke-width="3"/> <!-- Endpoints --> <circle cx="100" cy="275" r="4" fill="#f59e0b"/> <circle cx="340" cy="235" r="4" fill="#f59e0b"/> <text x="100" y="295" font-family="sans-serif" font-size="10" fill="#f59e0b" text-anchor="middle">a</text> <text x="340" y="255" font-family="sans-serif" font-size="10" fill="#f59e0b" text-anchor="middle">b</text> <!-- Absolute Max --> <circle cx="155" cy="208" r="5" fill="#e879f9" filter="url(#glow)"/> <text x="155" y="195" font-family="sans-serif" font-size="10" fill="#e879f9" text-anchor="middle" font-weight="bold">ABS MAX</text> <!-- Right Panel: MVT --> <rect x="470" y="110" width="390" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="490" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">II. Mean Value Theorem (MVT)</text> <text x="490" y="160" font-family="sans-serif" font-size="12" fill="#94a3b8">Instantaneous rate equals Average rate at point c.</text> <!-- MVT Mini-Graph --> <path d="M 520 300 Q 650 150 820 280" fill="none" stroke="#38bdf8" stroke-width="3"/> <!-- Secant Line --> <line x1="540" y1="275" x2="800" y2="265" stroke="#94a3b8" stroke-width="1" stroke-dasharray="5"/> <text x="670" y="285" font-family="sans-serif" font-size="10" fill="#94a3b8" text-anchor="middle">Secant (Avg Rate)</text> <!-- Tangent Line --> <line x1="600" y1="195" x2="740" y2="190" stroke="#38bdf8" stroke-width="2"/> <circle cx="670" cy="192" r="4" fill="#38bdf8" filter="url(#glow)"/> <text x="670" y="180" font-family="sans-serif" font-size="10" fill="#38bdf8" text-anchor="middle" font-weight="bold">f'(c)</text> <!-- Bottom Panel: Candidates Test --> <rect x="40" y="370" width="820" height="160" rx="16" fill="#ffffff05" stroke="#ffffff10"/> <text x="60" y="400" font-family="sans-serif" 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font-family="sans-serif" font-size="10" fill="#64748b">Cusps, Corners, Verticals</text> <!-- Column 3 --> <rect x="520" width="240" height="80" rx="8" fill="#ffffff08"/> <text x="640" y="30" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#e879f9">Boundary Points</text> <text x="640" y="55" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#94a3b8">x = a, x = b</text> <text x="640" y="70" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#64748b">Interval Endpoints</text> </g> <!-- Decorative Icons / Symbols --> <g opacity="0.2" transform="translate(820, 40)"> <circle cx="0" cy="0" r="30" fill="none" stroke="#38bdf8" stroke-width="1"/> <path d="M -15 0 L 15 0 M 0 -15 L 0 15" stroke="#38bdf8" stroke-width="1"/> </g> <!-- Footer Note --> <text x="450" y="545" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#475569">Calculus Section 4.1: Analytical Applications &amp; Optimization Theory</text> </svg>Analytical Applications of Differentiation image 1Analytical Applications of Differentiation - AP/College Calculus BC - image 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/analytical-applications-differentiation/svg/1Analytical Applications of Differentiation diagram 1Analytical Applications of Differentiation - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/analytical-applications-differentiation/svg/2Analytical Applications of Differentiation diagram 2Analytical Applications of Differentiation - AP/College Calculus BC - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path 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Discrete) --> <g transform="translate(40, 130)"> <rect width="260" height="380" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="130" y="40" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">DISCRETE FOUNDATION</text> <!-- Riemann Visual --> <g transform="translate(40, 70)"> <path d="M 0 100 Q 40 20 180 80" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4 2"/> <!-- Rectangles --> <rect x="10" y="72" width="30" height="28" fill="#38bdf844" stroke="#38bdf8" stroke-width="1"/> <rect x="40" y="45" width="30" height="55" fill="#38bdf844" stroke="#38bdf8" stroke-width="1"/> <rect x="70" y="38" width="30" height="62" fill="#38bdf844" stroke="#38bdf8" stroke-width="1"/> <rect x="100" y="48" width="30" height="52" fill="#38bdf844" stroke="#38bdf8" stroke-width="1"/> <rect x="130" y="62" width="30" height="38" fill="#38bdf844" stroke="#38bdf8" stroke-width="1"/> <line x1="0" y1="100" x2="180" y2="100" stroke="#f8fafc" stroke-width="1"/> </g> <text x="130" y="210" text-anchor="middle" font-family="serif" font-size="20" fill="#f8fafc">Σ f(xᵢ*) Δx</text> <text x="20" y="245" font-family="sans-serif" font-size="13" fill="#94a3b8"> <tspan x="20" dy="18">• Approximation via rectangles</tspan> <tspan x="20" dy="18">• Limit as n approaches infinity</tspan> <tspan x="20" dy="18">• Area under the curve</tspan> <tspan x="20" dy="18">• Error depends on sample points</tspan> </text> <rect x="30" y="335" width="200" height="30" rx="8" fill="#38bdf820"/> <text x="130" y="355" text-anchor="middle" font-family="sans-serif" font-weight="600" font-size="12" fill="#38bdf8">THE RIEMANN SUM</text> </g> <!-- Column 2: FTC (The Great Unification) --> <g transform="translate(320, 130)"> <rect width="260" height="380" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="130" y="40" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">THE UNIFICATION</text> <!-- FTC Visual: The Bridge --> <g transform="translate(50, 70)"> <path d="M 10 80 L 150 80" stroke="#e879f9" stroke-width="4" stroke-linecap="round"/> <path d="M 30 80 L 30 40 M 130 80 L 130 40" stroke="#e879f9" stroke-width="2"/> <circle cx="80" cy="40" r="25" fill="none" stroke="#e879f9" stroke-width="2" stroke-dasharray="2 2"/> <text x="80" y="45" text-anchor="middle" font-family="serif" font-size="18" fill="#f8fafc">FTC</text> </g> <text x="130" y="210" text-anchor="middle" font-family="serif" font-size="18" fill="#f8fafc">d/dx ∫ f(t) dt = f(x)</text> <text x="20" y="245" font-family="sans-serif" font-size="13" fill="#94a3b8"> <tspan x="20" dy="18">• Links derivatives &amp; integrals</tspan> <tspan x="20" dy="18">• Part 1: Accumulation rate</tspan> <tspan x="20" dy="18">• Part 2: Evaluation theorem</tspan> <tspan x="20" dy="18">• Inverse operations</tspan> </text> <rect x="30" y="335" width="200" height="30" rx="8" fill="#e879f920"/> <text x="130" y="355" text-anchor="middle" font-family="sans-serif" font-weight="600" font-size="12" fill="#e879f9">FUNDAMENTAL THEOREM</text> </g> <!-- Column 3: Definite Integral (The Continuous) --> <g transform="translate(600, 130)"> <rect width="260" height="380" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="130" y="40" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">CONTINUOUS WHOLE</text> <!-- Integral Visual --> <g transform="translate(40, 70)"> <path d="M 0 100 Q 40 20 180 80 L 180 100 L 0 100 Z" fill="#f59e0b33" stroke="#f59e0b" stroke-width="2"/> <line x1="0" y1="100" x2="180" y2="100" stroke="#f8fafc" stroke-width="1"/> <text x="90" y="115" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">[a, b]</text> </g> <text x="130" y="210" text-anchor="middle" font-family="serif" font-size="20" fill="#f8fafc">∫ₐᵇ f(x) dx = F(b) - F(a)</text> <text x="20" y="245" font-family="sans-serif" font-size="13" fill="#94a3b8"> <tspan x="20" dy="18">• Exact net change calculation</tspan> <tspan x="20" dy="18">• Total quantity reconstructed</tspan> <tspan x="20" dy="18">• Global behavior from local data</tspan> <tspan x="20" dy="18">• Sophisticated analytical tool</tspan> </text> <rect x="30" y="335" width="200" height="30" rx="8" fill="#f59e0b20"/> <text x="130" y="355" text-anchor="middle" font-family="sans-serif" font-weight="600" font-size="12" fill="#f59e0b">DEFINITE INTEGRAL</text> </g> <!-- Connecting Arrows --> <path d="M 300 320 L 320 320" stroke="#ffffff20" stroke-width="2" marker-end="url(#arrow)"/> <path d="M 580 320 L 600 320" stroke="#ffffff20" stroke-width="2" marker-end="url(#arrow)"/> <defs> <marker id="arrow" markerWidth="10" markerHeight="10" refX="9" refY="3" orient="auto" markerUnits="strokeWidth"> <path d="M0,0 L0,6 L9,3 z" fill="#ffffff20" /> </marker> </defs> <!-- Footer Info --> <rect x="40" y="525" width="820" height="1" fill="#ffffff10"/> <text x="40" y="545" font-family="sans-serif" font-size="11" fill="#64748b">CALCULUS BC: UNIT 6</text> <text x="860" y="545" text-anchor="end" font-family="sans-serif" font-size="11" fill="#64748b">INTEGRATION AND ACCUMULATION OF CHANGE</text> </svg>Integration and Accumulation of Change image 1Integration and Accumulation of Change - AP/College Calculus BC - image 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/integration-and-accumulation/svg/1Integration and Accumulation of Change diagram 1Integration and Accumulation of Change - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/differential-equations/svg/1Differential Equations diagram 1Differential Equations - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/applications-of-integration/svg/1Applications of Integration diagram 1Applications of Integration - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/applications-of-integration/svg/2Applications of Integration diagram 2Applications of Integration - AP/College Calculus BC - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/applications-of-integration/svg/3Applications of Integration diagram 3Applications of Integration - AP/College Calculus BC - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dotGrid" x="0" y="0" width="30" height="30" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" 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y2="280" stroke="#38bdf8" stroke-width="3" marker-end="url(#arrowhead)" context-fill="#38bdf8"/> <text x="455" y="295" font-family="serif" font-weight="bold" font-size="14" fill="#38bdf8">a(t)</text> <g transform="translate(340, 430)"> <text x="0" y="0" font-family="serif" font-size="14" fill="#f8fafc">r(t) = ⟨x(t), y(t)⟩</text> <text x="0" y="25" font-family="sans-serif" font-size="12" fill="#94a3b8">Total Distance Traveled:</text> <text x="0" y="45" font-family="serif" font-size="16" fill="#f8fafc">∫ |v(t)| dt</text> <text x="0" y="75" font-family="sans-serif" font-size="11" fill="#e879f9" font-style="italic">Modeling SpaceX Falcon 9 Trajectories</text> </g> <!-- Panel 3: Polar (Right) --> <rect x="610" y="110" width="260" height="420" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="740" y="145" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="20" fill="#f59e0b">POLAR</text> <text x="740" y="165" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#94a3b8">Angular Perspectives</text> <!-- Polar Illustration: Rose Curve --> <g transform="translate(740, 280)"> <circle r="80" fill="none" stroke="#ffffff10" stroke-width="1"/> <circle r="50" fill="none" stroke="#ffffff10" stroke-width="1"/> <line x1="-90" y1="0" x2="90" y2="0" stroke="#ffffff10"/> <line x1="0" y1="-90" x2="0" y2="90" stroke="#ffffff10"/> <!-- Rose Curve: r = cos(2theta) --> <path d="M 70 0 C 70 -50 20 -70 0 0 C -20 -70 -70 -50 -70 0 C -70 50 -20 70 0 0 C 20 70 70 50 70 0" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2" filter="url(#glow)"/> </g> <g transform="translate(630, 430)"> <text x="0" y="0" font-family="serif" font-size="14" fill="#f8fafc">r = f(θ)</text> <text x="0" y="25" font-family="sans-serif" font-size="12" fill="#94a3b8">Area in Polar:</text> <text x="0" y="45" font-family="serif" font-size="16" fill="#f8fafc">A = ½ ∫ [r(θ)]² dθ</text> <text x="0" y="75" font-family="sans-serif" font-size="11" fill="#f59e0b" font-style="italic">Electromagnetic Dipole Patterns</text> </g> <!-- Comparison Footer --> <rect x="30" y="540" width="840" height="20" rx="4" fill="#38bdf820"/> <text x="450" y="554" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#38bdf8" letter-spacing="1">TRANSITIONING FROM CARTESIAN: BEYOND THE VERTICAL LINE TEST</text> </svg>Parametric, Polar, and Vector Functions image 1Parametric, Polar, and Vector Functions - AP/College Calculus BC - image 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/parametric-polar-vector/svg/1Parametric, Polar, and Vector Functions diagram 1Parametric, Polar, and Vector Functions - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/parametric-polar-vector/svg/2Parametric, Polar, and Vector Functions diagram 2Parametric, Polar, and Vector Functions - AP/College Calculus BC - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/infinite-sequences-and-series/svg/1Infinite Sequences and Series diagram 1Infinite Sequences and Series - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/infinite-sequences-and-series/svg/2Infinite Sequences and Series diagram 2Infinite Sequences and Series - AP/College Calculus BC - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/infinite-sequences-and-series/svg/3Infinite Sequences and Series diagram 3Infinite Sequences and Series - AP/College Calculus BC - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="32" letter-spacing="1">AP CALCULUS BC: FRQ BLUEPRINT</text> <rect x="380" y="65" width="140" height="4" fill="#38bdf8" rx="2"/> <text x="450" y="85" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="500">THE ULTIMATE CRUCIBLE OF MATHEMATICAL MASTERY</text> <!-- Section 1: The Anatomy (Comparison) --> <g transform="translate(40, 110)"> <rect width="400" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="20" y="30" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="18">SECTION STRUCTURE</text> <!-- Part A --> <rect x="20" y="50" width="170" height="110" rx="12" fill="#38bdf815" stroke="#38bdf840"/> <text x="105" y="75" text-anchor="middle" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="16">PART A</text> <text x="105" y="95" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="12">2 Questions | 30 Mins</text> <rect x="55" y="105" width="100" height="20" rx="10" fill="#38bdf8"/> <text x="105" y="119" text-anchor="middle" fill="#0f172a" font-family="sans-serif" font-weight="800" font-size="10">CALC REQUIRED</text> <text x="105" y="140" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="10">Modeling &amp; Data Analysis</text> <!-- Part B --> <rect x="210" y="50" width="170" height="110" rx="12" fill="#f59e0b15" stroke="#f59e0b40"/> <text x="295" y="75" text-anchor="middle" fill="#f59e0b" font-family="sans-serif" font-weight="700" font-size="16">PART B</text> <text x="295" y="95" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="12">4 Questions | 60 Mins</text> <rect x="245" y="105" width="100" height="20" rx="10" fill="#f59e0b"/> <text x="295" y="119" text-anchor="middle" fill="#0f172a" font-family="sans-serif" font-weight="800" font-size="10">CALC PROHIBITED</text> <text x="295" y="140" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="10">Proofs &amp; Taylor Series</text> </g> <!-- Section 2: The 9-Point Rubric (Process) --> <g transform="translate(460, 110)"> <rect width="400" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="20" y="30" fill="#e879f9" font-family="sans-serif" font-weight="700" font-size="18">SCORING HEURISTICS</text> <!-- Rubric Steps --> <g transform="translate(20, 50)"> <circle cx="15" cy="10" r="12" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="15" y="14" text-anchor="middle" fill="#e879f9" font-family="sans-serif" font-weight="800" font-size="12">1</text> <text x="40" y="10" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="13">THE SETUP</text> <text x="40" y="25" fill="#94a3b8" font-family="sans-serif" font-size="11">Correct integral or derivative expression.</text> <circle cx="15" cy="50" r="12" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="15" y="54" text-anchor="middle" fill="#e879f9" font-family="sans-serif" font-weight="800" font-size="12">2</text> <text x="40" y="50" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="13">INTERMEDIATE STEPS</text> <text x="40" y="65" fill="#94a3b8" font-family="sans-serif" font-size="11">Application of theorems (MVT, IVT, etc.)</text> <circle cx="15" cy="90" r="12" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="15" y="94" text-anchor="middle" fill="#e879f9" font-family="sans-serif" font-weight="800" font-size="12">3</text> <text x="40" y="90" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="13">THE ANSWER &amp; JUSTIFICATION</text> <text x="40" y="105" fill="#94a3b8" font-family="sans-serif" font-size="11">Numerical value (3 decimals) + Sentence.</text> </g> </g> <!-- The Golden Rule Banner --> <g transform="translate(40, 310)"> <rect width="820" height="40" rx="8" fill="#ef444420" stroke="#ef4444" stroke-width="1"/> <path d="M20 20 L35 20" stroke="#ef4444" stroke-width="3" stroke-linecap="round"/> <text x="410" y="26" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="14"> <tspan fill="#ef4444">THE GOLDEN RULE:</tspan> NO "BALD ANSWERS". NO WORK = NO POINTS. </text> </g> <!-- Section 3: Problem Archetypes (Conceptual Map) --> <g transform="translate(40, 370)"> <text x="0" y="-10" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="18">STRATEGIC ARCHETYPES</text> <!-- Rate In/Out --> <rect x="0" y="10" width="195" height="140" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <circle cx="35" cy="45" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <path d="M30 45 L40 45 M35 40 L35 50" stroke="#38bdf8" stroke-width="2"/> <text x="60" y="50" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="14">Rate In / Out</text> <text x="20" y="80" fill="#f8fafc" font-family="sans-serif" font-size="11" font-weight="600">Accumulation Formula:</text> <text x="20" y="100" fill="#94a3b8" font-family="serif" font-style="italic" font-size="13">A(t) = A(0) + ∫[R(s)-E(s)]ds</text> <text x="20" y="125" fill="#94a3b8" font-family="sans-serif" font-size="10">Commonly Question 1 or 2.</text> <!-- Particle Motion --> <rect x="208" y="10" width="195" height="140" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <circle cx="243" cy="45" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="1.5"/> <path d="M238 45 L248 45 L245 42 M248 45 L245 48" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="268" y="50" fill="#e879f9" font-family="sans-serif" font-weight="700" font-size="14">Particle Motion</text> <text x="228" y="80" fill="#f8fafc" font-family="sans-serif" font-size="11" font-weight="600">Vector-Valued (BC):</text> <text x="228" y="100" fill="#94a3b8" font-family="serif" font-style="italic" font-size="13">Speed = √[x'(t)² + y'(t)²]</text> <text x="228" y="125" fill="#94a3b8" font-family="sans-serif" font-size="10">Focus on Total Distance.</text> <!-- Area & Volume --> <rect x="416" y="10" width="195" height="140" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <circle cx="451" cy="45" r="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <path d="M443 52 Q451 30 459 52" fill="none" stroke="#f59e0b" stroke-width="2"/> <text x="476" y="50" fill="#f59e0b" font-family="sans-serif" font-weight="700" font-size="14">Area &amp; Volume</text> <text x="436" y="80" fill="#f8fafc" font-family="sans-serif" font-size="11" font-weight="600">Polar &amp; Rotational:</text> <text x="436" y="100" fill="#94a3b8" font-family="serif" font-style="italic" font-size="13">Area = ½ ∫ [r(θ)]² dθ</text> <text x="436" y="125" fill="#94a3b8" font-family="sans-serif" font-size="10">Washers vs. Cross-sections.</text> <!-- Taylor Series --> <rect x="625" y="10" width="195" height="140" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <circle cx="660" cy="45" r="15" fill="#10b98120" stroke="#10b981" stroke-width="1.5"/> <text x="655" y="50" fill="#10b981" font-family="serif" font-weight="800" font-size="18">Σ</text> <text x="685" y="50" fill="#10b981" font-family="sans-serif" font-weight="700" font-size="14">Taylor Series</text> <text x="645" y="80" fill="#f8fafc" font-family="sans-serif" font-size="11" font-weight="600">The "Question 6":</text> <text x="645" y="100" fill="#94a3b8" font-family="serif" font-style="italic" font-size="13">fⁿ(c)/n! · (x-c)ⁿ</text> <text x="645" y="125" fill="#94a3b8" font-family="sans-serif" font-size="10">Lagrange Error Bound.</text> </g> <!-- Footer Branding --> <rect x="0" y="535" width="900" height="25" fill="#00000030"/> <text x="450" y="552" text-anchor="middle" fill="#475569" font-family="sans-serif" font-size="10" font-weight="600" letter-spacing="2">AP CALCULUS BC • FREE RESPONSE QUESTION STRATEGY GUIDE • COLLEGE BOARD STANDARDS</text> </svg>AP Exam Preparation (FRQs) image 1AP Exam Preparation (FRQs) - AP/College Calculus BC - image 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/ap-exam-preparation/svg/1AP Exam Preparation (FRQs) diagram 1AP Exam Preparation (FRQs) - AP/College Calculus BC - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/ap-exam-preparation/svg/2AP Exam Preparation (FRQs) diagram 2AP Exam Preparation (FRQs) - AP/College Calculus BC - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-bc-f0911bf9-0b0e-4390-9916-edee07cb9049/media/ap-exam-preparation/svg/3AP Exam Preparation (FRQs) diagram 3AP Exam Preparation (FRQs) - AP/College Calculus BC - diagram 3https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c2026-04-20T04:58:34.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#818cf8"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <!-- Subtle Grid Pattern --> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">LIMITS &amp; CONTINUITY FOUNDATIONS</text> <path d="M 350 65 L 550 65" stroke="url(#accentGrad)" stroke-width="3" stroke-linecap="round"/> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">The transition from static algebra to dynamic calculus</text> <!-- Left Column: The Limit Concept --> <rect x="40" y="110" width="400" height="200" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">1. THE DYNAMIC APPROACH</text> <text x="60" y="165" font-family="sans-serif" font-size="13" fill="#f8fafc">Algebra asks: "What is the value at x?"</text> <text x="60" y="182" font-family="sans-serif" font-size="13" fill="#f8fafc">Calculus asks: "What happens as we get close?"</text> <!-- Limit Visualization --> <g transform="translate(60, 210)"> <path d="M 0 60 L 150 60 M 10 0 L 10 70" stroke="#94a3b8" stroke-width="1" fill="none"/> <path d="M 10 50 Q 60 45, 140 10" stroke="#f59e0b" stroke-width="2" fill="none"/> <circle cx="80" cy="38" r="4" fill="none" stroke="#f59e0b" stroke-width="2"/> <!-- Hole --> <text x="160" y="20" font-family="sans-serif" font-size="12" fill="#f8fafc" font-weight="bold">lim f(x) = L</text> <text x="160" y="35" font-family="sans-serif" font-size="11" fill="#94a3b8">x → c</text> <!-- Arrows --> <path d="M 50 65 L 75 65" stroke="#38bdf8" stroke-width="2" marker-end="url(#arrow)"/> <path d="M 110 65 L 85 65" stroke="#38bdf8" stroke-width="2" marker-end="url(#arrow)"/> <text x="75" y="80" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#38bdf8">x approaches c</text> </g> <!-- Right Column: Continuity Checklist --> <rect x="460" y="110" width="400" height="200" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="480" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">2. CONTINUITY CHECKLIST</text> <g transform="translate(480, 165)"> <circle cx="10" cy="5" r="8" fill="#e879f920" stroke="#e879f9" stroke-width="1"/> <text x="25" y="10" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="600">f(c) is Defined</text> <text x="25" y="25" font-family="sans-serif" font-size="11" fill="#94a3b8">The point exists in the domain.</text> <circle cx="10" cy="50" r="8" fill="#e879f920" stroke="#e879f9" stroke-width="1"/> <text x="25" y="55" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="600">Limit Exists</text> <text x="25" y="70" font-family="sans-serif" font-size="11" fill="#94a3b8">Left-hand limit = Right-hand limit.</text> <circle cx="10" cy="95" r="8" fill="#e879f920" stroke="#e879f9" stroke-width="1"/> <text x="25" y="100" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="600">Limit = Value</text> <text x="25" y="115" font-family="sans-serif" font-size="11" fill="#94a3b8">The "hole" is filled by the actual point.</text> </g> <!-- Bottom Section: Discontinuity Types --> <rect x="40" y="330" width="820" height="190" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="360" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">3. TYPES OF DISCONTINUITY</text> <!-- Discontinuity 1: Removable --> <g transform="translate(80, 380)"> <path d="M 0 80 L 120 80 M 10 10 L 10 90" stroke="#ffffff30" stroke-width="1"/> <path d="M 20 70 Q 60 65, 110 30" stroke="#38bdf8" stroke-width="2" fill="none"/> <circle cx="65" cy="61" r="4" fill="#1e1b4b" stroke="#38bdf8" stroke-width="2"/> <circle cx="65" cy="30" r="3" fill="#38bdf8"/> <text x="60" y="105" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#f8fafc" font-weight="bold">REMOVABLE</text> <text x="60" y="120" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">"The Hole"</text> </g> <!-- Discontinuity 2: Jump --> <g transform="translate(350, 380)"> <path d="M 0 80 L 120 80 M 10 10 L 10 90" stroke="#ffffff30" stroke-width="1"/> <path d="M 20 70 L 60 50" stroke="#e879f9" stroke-width="2" fill="none"/> <path d="M 60 20 L 110 10" stroke="#e879f9" stroke-width="2" fill="none"/> <circle cx="60" cy="50" r="3" fill="#e879f9"/> <circle cx="60" cy="20" r="3" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="60" y="105" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#f8fafc" font-weight="bold">JUMP</text> <text x="60" y="120" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">Piecewise Breaks</text> </g> <!-- Discontinuity 3: Infinite --> <g transform="translate(620, 380)"> <path d="M 0 80 L 120 80 M 10 10 L 10 90" stroke="#ffffff30" stroke-width="1"/> <path d="M 60 10 L 60 90" stroke="#ffffff40" stroke-dasharray="4" stroke-width="1"/> <path d="M 20 75 Q 50 70, 55 10" stroke="#f59e0b" stroke-width="2" fill="none"/> <path d="M 65 90 Q 70 30, 110 25" stroke="#f59e0b" stroke-width="2" fill="none"/> <text x="60" y="105" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#f8fafc" font-weight="bold">INFINITE</text> <text x="60" y="120" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">Vertical Asymptotes</text> </g> <!-- Formal Definition Box (Small Overlay) --> <rect x="600" y="235" width="240" height="60" rx="8" fill="#38bdf815" stroke="#38bdf840"/> <text x="610" y="255" font-family="serif" font-style="italic" font-size="12" fill="#38bdf8">ε-δ Definition</text> <text x="610" y="275" font-family="serif" font-size="11" fill="#f8fafc">|x - c| &lt; δ ⇒ |f(x) - L| &lt; ε</text> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="url(#accentGrad)" opacity="0.1"/> <circle cx="50" cy="510" r="20" fill="#e879f9" opacity="0.1"/> <!-- Marker for arrows --> <defs> <marker id="arrow" markerWidth="10" markerHeight="10" refX="9" refY="3" orientation="auto" markerUnits="strokeWidth"> <path d="M0,0 L0,6 L9,3 z" fill="#38bdf8" /> </marker> </defs> </svg>Limits and Continuity Foundations image 1Limits and Continuity Foundations - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/limits-and-continuity-foundations/svg/1Limits and Continuity Foundations diagram 1Limits and Continuity Foundations - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/limits-and-continuity-foundations/svg/2Limits and Continuity Foundations diagram 2Limits and Continuity Foundations - AP/College Calculus AB - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <filter id="shadow" x="-20%" y="-20%" width="140%" height="140%"> <feDropShadow dx="0" dy="4" stdDeviation="8" flood-opacity="0.5"/> </filter> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">ESTIMATING LIMITS</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-weight="400" font-size="16" fill="#94a3b8" letter-spacing="2">NUMERICAL &amp; GRAPHICAL ANALYSIS</text> <rect x="400" y="95" width="100" height="3" rx="1.5" fill="#f59e0b"/> <!-- Left Card: The Concept --> <g transform="translate(40, 120)" filter="url(#shadow)"> <rect width="260" height="400" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <circle cx="40" cy="40" r="18" fill="#f59e0b20"/> <path d="M 35 40 L 45 40 M 40 35 L 40 45" stroke="#f59e0b" stroke-width="2" fill="none"/> <text x="70" y="45" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">THE CONCEPT</text> <text x="25" y="90" font-family="sans-serif" font-size="13" fill="#94a3b8" font-style="italic">"The Journey, Not the Destination"</text> <rect x="25" y="115" width="210" height="80" rx="8" fill="#00000030"/> <text x="130" y="150" text-anchor="middle" font-family="serif" font-size="24" fill="#f8fafc">lim</text> <text x="130" y="165" text-anchor="middle" font-family="serif" font-size="12" fill="#f8fafc">x → a</text> <text x="175" y="155" text-anchor="middle" font-family="serif" font-size="24" fill="#f8fafc">f(x) = L</text> <text x="25" y="225" font-family="sans-serif" font-size="13" fill="#cbd5e1" line-height="1.5"> <tspan x="25" dy="0">• Focuses on the neighborhood</tspan> <tspan x="25" dy="22">• f(a) need not be defined</tspan> <tspan x="25" dy="22">• Approaches from both sides</tspan> <tspan x="25" dy="22">• Describes local behavior</tspan> </text> <path d="M 40 340 Q 130 310 220 340" stroke="#f59e0b" stroke-width="2" fill="none" stroke-dasharray="4 2"/> <circle cx="130" cy="325" r="5" stroke="#f59e0b" stroke-width="2" fill="none"/> <text x="130" y="360" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#94a3b8">Target Value (L)</text> </g> <!-- Middle Card: Numerical --> <g transform="translate(320, 120)" filter="url(#shadow)"> <rect width="260" height="400" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <circle cx="40" cy="40" r="18" fill="#38bdf820"/> <rect x="34" y="34" width="12" height="12" stroke="#38bdf8" stroke-width="2" fill="none"/> <text x="70" y="45" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">NUMERICAL</text> <text x="25" y="85" font-family="sans-serif" font-size="13" fill="#94a3b8">The "Delta-Stepping" Table</text> <!-- Table Mockup --> <g transform="translate(25, 110)"> <rect width="210" height="180" rx="8" fill="#00000030"/> <line x1="105" y1="10" x2="105" y2="170" stroke="#ffffff20" stroke-width="1"/> <line x1="10" y1="40" x2="200" y2="40" stroke="#ffffff20" stroke-width="1"/> <text x="52" y="28" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">x</text> <text x="157" y="28" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">f(x)</text> <text x="52" y="65" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">0.9</text> <text x="157" y="65" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">1.9000</text> <text x="52" y="90" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">0.99</text> <text x="157" y="90" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">1.9900</text> <text x="52" y="115" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#e879f9" font-weight="bold">1.0</text> <text x="157" y="115" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#e879f9" font-weight="bold">???</text> <text x="52" y="140" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">1.01</text> <text x="157" y="140" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">2.0100</text> <text x="52" y="165" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">1.1</text> <text x="157" y="165" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">2.1000</text> </g> <text x="25" y="320" font-family="sans-serif" font-size="12" fill="#cbd5e1" line-height="1.4"> <tspan x="25" dy="0">Step 1: Choose values closer to 'a'</tspan> <tspan x="25" dy="20">Step 2: Evaluate from Left &amp; Right</tspan> <tspan x="25" dy="20">Step 3: Check if values converge</tspan> </text> <path d="M 110 375 L 150 375" stroke="#38bdf8" stroke-width="2" fill="none" marker-end="url(#arrow)"/> <text x="130" y="392" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#38bdf8">CONVERGENCE</text> </g> <!-- Right Card: Graphical --> <g transform="translate(600, 120)" filter="url(#shadow)"> <rect width="260" height="400" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <circle cx="40" cy="40" r="18" fill="#e879f920"/> <path d="M 32 45 L 40 35 L 48 45" stroke="#e879f9" stroke-width="2" fill="none"/> <text x="70" y="45" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">GRAPHICAL</text> <text x="25" y="85" font-family="sans-serif" font-size="13" fill="#94a3b8">Visualizing Discontinuities</text> <!-- Graph Mockup --> <g transform="translate(30, 110)"> <rect width="200" height="150" rx="4" fill="#00000030"/> <!-- Axes --> <line x1="20" y1="130" x2="180" y2="130" stroke="#ffffff40" stroke-width="1"/> <line x1="30" y1="20" x2="30" y2="140" stroke="#ffffff40" stroke-width="1"/> <!-- Function Curve --> <path d="M 40 110 Q 100 80 160 30" stroke="#e879f9" stroke-width="3" fill="none"/> <!-- Hole --> <circle cx="100" cy="80" r="5" fill="#1e1b4b" stroke="#e879f9" stroke-width="2"/> <!-- Approach Arrows --> <path d="M 70 100 L 90 88" stroke="#38bdf8" stroke-width="2" fill="none" marker-end="url(#arrowhead)"/> <path d="M 130 60 L 110 72" stroke="#38bdf8" stroke-width="2" fill="none" marker-end="url(#arrowhead)"/> <text x="100" y="145" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">x = a</text> <text x="15" y="80" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8" transform="rotate(-90, 15, 80)">L</text> </g> <g transform="translate(25, 280)"> <rect x="0" y="0" width="10" height="10" rx="2" fill="#e879f9"/> <text x="20" y="10" font-family="sans-serif" font-size="12" fill="#cbd5e1">Holes (Removable)</text> <rect x="0" y="25" width="10" height="10" rx="2" fill="#f59e0b"/> <text x="20" y="35" font-family="sans-serif" font-size="12" fill="#cbd5e1">Jumps (DNE)</text> <rect x="0" y="50" width="10" height="10" rx="2" fill="#38bdf8"/> <text x="20" y="60" font-family="sans-serif" font-size="12" fill="#cbd5e1">Asymptotes (Infinite)</text> </g> <text x="25" y="375" font-family="sans-serif" font-size="11" fill="#94a3b8" font-style="italic"> "Trace the path from both sides. If they meet at the same height, the limit exists." </text> </g> <!-- Markers --> <defs> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="#38bdf8" /> </marker> </defs> <!-- Footer Info --> <rect x="40" y="535" width="820" height="1" fill="#ffffff15"/> <text x="450" y="552" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#64748b" letter-spacing="1">CALCULUS FUNDAMENTALS • SECTION 1.2 • WIKI ILLUSTRATED SERIES</text> </svg>Estimating Limits Numerically and Graphically image 1Estimating Limits Numerically and Graphically - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/estimating-limits/svg/1Estimating Limits Numerically and Graphically diagram 1Estimating Limits Numerically and Graphically - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/estimating-limits/svg/2Estimating Limits Numerically and Graphically diagram 2Estimating Limits Numerically and Graphically - AP/College Calculus AB - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="cardGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#ffffff15"/> <stop offset="100%" stop-color="#ffffff05"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Subtle Grid Lines --> <path d="M 0 100 L 900 100 M 0 480 L 900 480" stroke="#ffffff10" stroke-width="1"/> <!-- Header Section --> <text x="450" y="55" text-anchor="middle" fill="#f8fafc" font-family="system-ui, sans-serif" font-size="34" font-weight="800" letter-spacing="1">DIFFERENTIATION</text> <text x="450" y="82" text-anchor="middle" fill="#38bdf8" font-family="system-ui, sans-serif" font-size="16" font-weight="500" letter-spacing="3">DEFINITION &amp; FUNDAMENTAL RULES</text> <!-- Card 1: The Limit Definition --> <rect x="40" y="120" width="260" height="340" rx="16" fill="url(#cardGrad)" stroke="#ffffff20"/> <text x="60" y="150" fill="#f59e0b" font-family="system-ui, sans-serif" font-size="14" font-weight="bold">01. THE FORMAL LIMIT</text> <!-- Graph Illustration --> <path d="M 70 260 Q 130 180 250 220" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4"/> <circle cx="110" cy="215" r="4" fill="#e879f9"/> <circle cx="180" cy="205" r="4" fill="#38bdf8"/> <line x1="80" y1="220" x2="230" y2="200" stroke="#f8fafc" stroke-width="1.5" filter="url(#glow)"/> <text x="110" y="280" fill="#94a3b8" font-family="serif" font-size="12" font-style="italic">h → 0</text> <text x="60" y="330" fill="#f8fafc" font-family="serif" font-size="18">f'(x) = lim [f(x+h) - f(x)] / h</text> <text x="60" y="360" fill="#94a3b8" font-family="system-ui, sans-serif" font-size="12" width="220"> <tspan x="60" dy="1.2em">The derivative captures the</tspan> <tspan x="60" dy="1.2em">instantaneous rate of change</tspan> <tspan x="60" dy="1.2em">as the interval h vanishes.</tspan> </text> <!-- Card 2: Physical Interpretation --> <rect x="320" y="120" width="260" height="340" rx="16" fill="url(#cardGrad)" stroke="#ffffff20"/> <text x="340" y="150" fill="#38bdf8" font-family="system-ui, sans-serif" font-size="14" font-weight="bold">02. DYNAMICS &amp; MOTION</text> <!-- Motion Icons --> <g transform="translate(340, 180)"> <rect width="220" height="40" rx="8" fill="#ffffff10"/> <text x="10" y="25" fill="#f8fafc" font-family="system-ui, sans-serif" font-size="12">Position: s(t)</text> <path d="M 180 20 L 200 20" stroke="#38bdf8" stroke-width="2" marker-end="url(#arrow)"/> <rect y="50" width="220" height="40" rx="8" fill="#ffffff10"/> <text x="10" y="75" fill="#f8fafc" font-family="system-ui, sans-serif" font-size="12">Velocity: v(t) = s'(t)</text> <rect y="100" width="220" height="40" rx="8" fill="#ffffff10"/> <text x="10" y="125" fill="#f8fafc" font-family="system-ui, sans-serif" font-size="12">Accel: a(t) = v'(t)</text> </g> <text x="340" y="360" fill="#94a3b8" font-family="system-ui, sans-serif" font-size="12"> <tspan x="340" dy="1.2em">Calculus bridges the gap</tspan> <tspan x="340" dy="1.2em">between static algebra and</tspan> <tspan x="340" dy="1.2em">the physics of moving bodies.</tspan> </text> <!-- Card 3: The Power Rule --> <rect x="600" y="120" width="260" height="340" rx="16" fill="url(#cardGrad)" stroke="#ffffff20"/> <text x="620" y="150" fill="#e879f9" font-family="system-ui, sans-serif" font-size="14" font-weight="bold">03. THE POWER RULE</text> <g transform="translate(620, 180)"> <rect width="220" height="80" rx="12" fill="#e879f920" stroke="#e879f940"/> <text x="110" y="48" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="24" font-weight="bold">d/dx [xⁿ] = nxⁿ⁻¹</text> </g> <g transform="translate(620, 280)" font-family="monospace" font-size="13"> <text x="0" y="20" fill="#38bdf8">f(x) = x³</text> <text x="120" y="20" fill="#94a3b8">→ 3x²</text> <text x="0" y="45" fill="#38bdf8">f(x) = √x</text> <text x="120" y="45" fill="#94a3b8">→ ½x⁻½</text> <text x="0" y="70" fill="#38bdf8">f(x) = 1/x</text> <text x="120" y="70" fill="#94a3b8">→ -x⁻²</text> </g> <!-- Footer / Continuity Note --> <rect x="40" y="485" width="820" height="50" rx="12" fill="#ffffff05"/> <circle cx="65" cy="510" r="6" fill="#ef4444"/> <text x="85" y="515" fill="#94a3b8" font-family="system-ui, sans-serif" font-size="13"> <tspan fill="#f8fafc" font-weight="bold">CRITICAL NOTE:</tspan> Differentiability requires continuity, but continuity does not guarantee differentiability (e.g., sharp corners). </text> <!-- Decorative Accents --> <circle cx="850" cy="50" r="30" fill="none" stroke="#38bdf8" stroke-width="0.5" stroke-dasharray="2 2"/> <path d="M 40 40 L 60 40 M 40 40 L 40 60" stroke="#f59e0b" stroke-width="2"/> </svg>Differentiation: Definition and Fundamental Rules image 1Differentiation: Definition and Fundamental Rules - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/differentiation-foundations/svg/1Differentiation: Definition and Fundamental Rules diagram 1Differentiation: Definition and Fundamental Rules - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/differentiation-foundations/svg/2Differentiation: Definition and Fundamental Rules diagram 2Differentiation: Definition and Fundamental Rules - AP/College Calculus AB - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Decorative Elements --> <circle cx="850" cy="50" r="100" fill="#38bdf8" fill-opacity="0.05"/> <circle cx="50" cy="510" r="80" fill="#e879f9" fill-opacity="0.05"/> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="bold" fill="#f8fafc" letter-spacing="1">ADVANCED DIFFERENTIATION</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="16" fill="#94a3b8" font-weight="300">NAVIGATING NESTED SYSTEMS &amp; INTERTWINED VARIABLES</text> <rect x="400" y="100" width="100" height="3" rx="1.5" fill="#f59e0b"/> <!-- Left Panel: Chain Rule --> <rect x="40" y="130" width="400" height="310" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="70" y="170" font-family="sans-serif" font-size="20" font-weight="bold" fill="#38bdf8">The Chain Rule</text> <text x="70" y="192" font-family="sans-serif" font-size="13" fill="#94a3b8">The Calculus of Nested Systems</text> <!-- Chain Rule Visual: Nested Circles --> <circle cx="110" cy="260" r="35" fill="none" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2"/> <circle cx="110" cy="260" r="20" fill="#38bdf8" fill-opacity="0.2" stroke="#38bdf8" stroke-width="2"/> <text x="160" y="255" font-family="serif" font-style="italic" font-size="18" fill="#f8fafc">f ( g ( x ) )</text> <path d="M 160 265 L 240 265" stroke="#94a3b8" stroke-width="1" marker-end="url(#arrow)"/> <!-- Notation Cards --> <rect x="70" y="315" width="340" height="45" rx="8" fill="#00000030"/> <text x="85" y="343" font-family="serif" font-size="15" fill="#f8fafc">Lagrange: h'(x) = f'(g(x)) · g'(x)</text> <rect x="70" y="370" width="340" height="45" rx="8" fill="#00000030"/> <text x="85" y="398" font-family="serif" font-size="15" fill="#f8fafc">Leibniz: dy/dx = (dy/du) · (du/dx)</text> <!-- Right Panel: Implicit Differentiation --> <rect x="460" y="130" width="400" height="310" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="490" y="170" font-family="sans-serif" font-size="20" font-weight="bold" fill="#f59e0b">Implicit Differentiation</text> <text x="490" y="192" font-family="sans-serif" font-size="13" fill="#94a3b8">The Calculus of Intertwined Relations</text> <!-- Implicit Visual: Interlocking Rings --> <circle cx="530" cy="260" r="25" fill="none" stroke="#f59e0b" stroke-width="3"/> <circle cx="555" cy="260" r="25" fill="none" stroke="#e879f9" stroke-width="3"/> <text x="600" y="255" font-family="serif" font-style="italic" font-size="18" fill="#f8fafc">x² + y² = r²</text> <text x="600" y="275" font-family="sans-serif" font-size="11" fill="#94a3b8">y is hidden within the structure</text> <!-- Process Steps --> <g font-family="sans-serif" font-size="12" fill="#f8fafc"> <circle cx="500" cy="330" r="10" fill="#f59e0b"/> <text x="497" y="334" font-size="10" font-weight="bold">1</text> <text x="520" y="335">Differentiate both sides w.r.t. x</text> <circle cx="500" cy="360" r="10" fill="#f59e0b"/> <text x="497" y="364" font-size="10" font-weight="bold">2</text> <text x="520" y="365">Apply Chain Rule to all 'y' terms</text> <circle cx="500" cy="390" r="10" fill="#f59e0b"/> <text x="497" y="394" font-size="10" font-weight="bold">3</text> <text x="520" y="395">Isolate dy/dx algebraically</text> </g> <!-- Bottom Section: Applications --> <rect x="40" y="460" width="820" height="70" rx="16" fill="#ffffff05" stroke="#ffffff10" stroke-width="1"/> <text x="60" y="485" font-family="sans-serif" font-size="14" font-weight="bold" fill="#94a3b8" text-transform="uppercase">Real-World Applications</text> <g transform="translate(60, 505)"> <rect width="240" height="12" rx="6" fill="#38bdf820"/> <circle cx="6" cy="6" r="4" fill="#38bdf8"/> <text x="20" y="10" font-family="sans-serif" font-size="11" fill="#f8fafc">Neural Networks (Backpropagation)</text> <rect x="260" width="240" height="12" rx="6" fill="#e879f920"/> <circle cx="266" cy="6" r="4" fill="#e879f9"/> <text x="280" y="10" font-family="sans-serif" font-size="11" fill="#f8fafc">Orbital Mechanics &amp; Aerospace</text> <rect x="520" width="240" height="12" rx="6" fill="#f59e0b20"/> <circle cx="526" cy="6" r="4" fill="#f59e0b"/> <text x="540" y="10" font-family="sans-serif" font-size="11" fill="#f8fafc">Sensitivity in Financial Derivatives</text> </g> <!-- Decorative Accents --> <path d="M 450 130 L 450 440" stroke="#ffffff10" stroke-width="1" stroke-dasharray="5 5"/> <circle cx="450" cy="285" r="4" fill="#f59e0b" filter="glow"/> </svg>Advanced Differentiation: Chain Rule and Implicit Differentiation image 1Advanced Differentiation: Chain Rule and Implicit Differentiation - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/advanced-differentiation/svg/1Advanced Differentiation: Chain Rule and Implicit Differentiation diagram 1Advanced Differentiation: Chain Rule and Implicit Differentiation - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/advanced-differentiation/svg/2Advanced Differentiation: Chain Rule and Implicit Differentiation diagram 2Advanced Differentiation: Chain Rule and Implicit Differentiation - AP/College Calculus AB - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="32" letter-spacing="1">CONTEXTUAL APPLICATIONS OF DIFFERENTIATION</text> <text x="450" y="85" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="16" font-weight="300">The Bridge from Theoretical Mechanics to Dynamic Reality</text> <line x1="300" y1="105" x2="600" y2="105" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 4" opacity="0.5"/> <!-- Card 1: Kinematics --> <rect x="40" y="130" width="400" height="185" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="160" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="18">1. STRAIGHT-LINE MOTION</text> <text x="60" y="180" fill="#94a3b8" font-family="sans-serif" font-size="12">The Kinematic Hierarchy (Rectilinear Motion)</text> <!-- Kinematics Illustration --> <line x1="70" y1="230" x2="380" y2="230" stroke="#475569" stroke-width="2"/> <circle cx="220" cy="230" r="6" fill="#38bdf8" filter="url(#glow)"/> <path d="M 226 230 L 300 230" stroke="#38bdf8" stroke-width="3" marker-end="url(#arrow-blue)"/> <text x="70" y="220" fill="#f8fafc" font-family="monospace" font-size="11">s(t)</text> <text x="250" y="220" fill="#38bdf8" font-family="monospace" font-size="11">v(t) = s'(t)</text> <text x="250" y="250" fill="#e879f9" font-family="monospace" font-size="11">a(t) = v'(t)</text> <text x="60" y="285" fill="#f8fafc" font-family="sans-serif" font-size="11" opacity="0.8"> <tspan x="60" dy="0">• v(t) &gt; 0: Moving Right</tspan> <tspan x="200" dy="0">• v(t) &amp; a(t) same sign: Speeding Up</tspan> </text> <!-- Card 2: Related Rates --> <rect x="460" y="130" width="400" height="185" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="480" y="160" fill="#f59e0b" font-family="sans-serif" font-weight="700" font-size="18">2. 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Applications of Differentiation - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/contextual-applications-differentiation/svg/2Contextual Applications of Differentiation diagram 2Contextual Applications of Differentiation - AP/College Calculus AB - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/analytical-applications-differentiation/svg/1Analytical Applications of Differentiation diagram 1Analytical Applications of Differentiation - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/analytical-applications-differentiation/svg/2Analytical Applications of Differentiation diagram 2Analytical Applications of Differentiation - AP/College Calculus AB - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/analytical-applications-differentiation/svg/3Analytical Applications of Differentiation diagram 3Analytical Applications of Differentiation - AP/College Calculus AB - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bgGradient" x1="0%" y1="0%" x2="0%" y2="100%"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bgGradient)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="32" letter-spacing="1">INTEGRATION &amp; ACCUMULATION</text> <text x="450" y="75" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="400">THE MATHEMATICAL ENGINE OF GLOBAL CHANGE</text> <line x1="350" y1="85" x2="550" y2="85" stroke="#38bdf8" stroke-width="2" stroke-linecap="round" opacity="0.6"/> <!-- Left Card: The Concept --> <rect x="40" y="110" width="260" height="220" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="140" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="18">THE PERSPECTIVE</text> <text x="60" y="165" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="600">Local vs. Global</text> <!-- Mini Diagram: Derivative vs Integral --> <path d="M 70 260 Q 120 180 200 250" fill="none" stroke="#94a3b8" stroke-width="2"/> <!-- Shaded Area --> <path d="M 100 220 Q 120 180 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stroke="#e879f9"/> <text x="110" y="25" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="600">MIDPOINT</text> <text x="110" y="40" fill="#94a3b8" font-family="sans-serif" font-size="10">Center Sample</text> </g> <text x="450" y="500" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="11" font-style="italic">As n → ∞, Sum → Integral</text> <!-- Right Card: Physics & Definition --> <rect x="600" y="110" width="260" height="220" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="140" fill="#e879f9" font-family="sans-serif" font-weight="700" font-size="18">PHYSICS BRIDGE</text> <!-- Velocity Graph --> <g transform="translate(630, 160)"> <line x1="0" y1="80" x2="100" y2="80" stroke="#94a3b8" stroke-width="1"/> <line x1="0" y1="0" x2="0" y2="80" stroke="#94a3b8" stroke-width="1"/> <path d="M 0 60 C 20 20, 60 10, 100 40" fill="none" stroke="#e879f9" stroke-width="2"/> <path d="M 20 45 C 40 20, 60 15, 80 30 L 80 80 L 20 80 Z" fill="#e879f930"/> <text x="105" y="85" fill="#94a3b8" font-family="sans-serif" font-size="10">t</text> <text x="-15" y="10" fill="#94a3b8" font-family="sans-serif" font-size="10">v(t)</text> <text x="50" y="65" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="700" text-anchor="middle">Δ Displacement</text> </g> <text x="620" y="270" fill="#94a3b8" font-family="sans-serif" font-size="11"> <tspan x="620" dy="1.2em">The area under a velocity-time</tspan> <tspan x="620" dy="1.2em">graph represents the total change</tspan> <tspan x="620" dy="1.2em">in position (displacement).</tspan> </text> <!-- Bottom Formula Card --> <rect x="40" y="350" width="260" height="170" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="385" fill="#4ade80" font-family="sans-serif" font-weight="700" font-size="18">THE DEFINITION</text> <!-- Integral Symbol Graphic --> <text x="60" y="440" fill="#f8fafc" font-family="serif" font-size="40" font-style="italic">∫</text> <text x="75" y="415" fill="#f8fafc" font-family="serif" font-size="14">b</text> <text x="70" y="455" fill="#f8fafc" font-family="serif" font-size="14">a</text> <text x="95" y="440" fill="#f8fafc" font-family="serif" font-size="24">f(x) dx</text> <text x="60" y="485" fill="#94a3b8" font-family="sans-serif" font-size="11"> <tspan x="60" dy="1.2em">The limit of the Riemann sum</tspan> <tspan x="60" dy="1.2em">as the width of subintervals</tspan> <tspan x="60" dy="1.2em">approaches zero.</tspan> </text> <!-- Decorative Accents --> <circle cx="850" cy="50" r="30" fill="#38bdf8" opacity="0.1"/> <circle cx="50" cy="510" r="40" fill="#f59e0b" opacity="0.05"/> <path d="M 800 450 L 840 490 M 840 450 L 800 490" stroke="#ffffff10" stroke-width="4"/> <!-- Properties Box (Bottom Right) --> <rect x="600" y="350" width="260" height="170" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="380" fill="#94a3b8" font-family="sans-serif" font-weight="700" font-size="14">KEY PROPERTIES</text> <g font-family="sans-serif" font-size="11" fill="#f8fafc"> <text x="620" y="410">Additivity: ∫[a,b] + ∫[b,c] = ∫[a,c]</text> <text x="620" y="435">Linearity: ∫(kf + g) = k∫f + ∫g</text> <text x="620" y="460">Reversal: ∫[a,b] = -∫[b,a]</text> <text x="620" y="485">Zero Width: ∫[a,a] = 0</text> </g> </svg>Integration and Accumulation of Change image 1Integration and Accumulation of Change - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/integration-accumulation/svg/1Integration and Accumulation of Change diagram 1Integration and Accumulation of Change - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/integration-accumulation/svg/2Integration and Accumulation of Change diagram 2Integration and Accumulation of Change - AP/College Calculus AB - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> </defs> <!-- Background and Texture --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Subtle Grid Lines --> <g stroke="#ffffff08" stroke-width="1"> <line x1="0" y1="80" x2="900" y2="80" /> <line x1="0" y1="480" x2="900" y2="480" /> </g> <!-- Header Section --> <text x="40" y="50" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc">DIFFERENTIAL EQUATIONS &amp; MODELING</text> <text x="40" y="72" font-family="Arial, sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">MAPPING THE MATHEMATICS OF CHANGE</text> <rect x="740" y="35" width="120" height="24" rx="12" fill="#38bdf820" stroke="#38bdf8" stroke-width="1"/> <text x="800" y="51" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#38bdf8" text-anchor="middle">CALCULUS II / III</text> <!-- Left Panel: Slope Fields (Visual Analysis) --> <rect x="40" y="110" width="260" height="340" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="140" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">Visualizing the Flow</text> <text x="60" y="160" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Slope Fields: dy/dx = f(x,y)</text> <!-- Slope Field Illustration --> <g transform="translate(70, 180)"> <rect width="200" height="150" fill="#00000030" rx="8"/> <!-- Grid of slope segments --> <g stroke="#38bdf8" stroke-width="2" stroke-linecap="round"> <!-- Row 1 --> <line x1="20" 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sans-serif" font-size="12" fill="#f8fafc" width="220"> <tspan x="60" dy="1.2em">Qualitative analysis allows us to</tspan> <tspan x="60" dy="1.2em">see solution behavior without</tspan> <tspan x="60" dy="1.2em">solving the equation algebraically.</tspan> </text> <!-- Center Panel: The Anatomy (Definitions) --> <rect x="320" y="110" width="260" height="340" rx="16" fill="#ffffff10" stroke="#ffffff20"/> <text x="340" y="140" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#f59e0b">The Anatomy</text> <g transform="translate(340, 165)"> <rect width="220" height="60" rx="8" fill="#f59e0b15"/> <text x="10" y="25" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f59e0b">General Solution</text> <text x="10" y="45" font-family="serif" font-size="14" fill="#f8fafc">y = f(x) + C</text> <text x="210" y="45" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8" text-anchor="end">Family of Curves</text> </g> <g transform="translate(340, 235)"> <rect width="220" height="60" rx="8" fill="#e879f915"/> <text x="10" y="25" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#e879f9">Initial Condition</text> <text x="10" y="45" font-family="serif" font-size="14" fill="#f8fafc">y(x₀) = y₀</text> <text x="210" y="45" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8" text-anchor="end">Specific Point</text> </g> <g transform="translate(340, 305)"> <rect width="220" height="60" rx="8" fill="#38bdf815"/> <text x="10" y="25" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#38bdf8">Particular Solution</text> <text x="10" y="45" font-family="serif" font-size="14" fill="#f8fafc">y = f(x) + 5</text> <text x="210" y="45" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8" text-anchor="end">Unique Curve</text> </g> <text x="450" y="410" font-family="Arial, sans-serif" font-size="11" font-style="italic" fill="#94a3b8" text-anchor="middle">"Nature is written in the language of</text> <text x="450" y="425" font-family="Arial, sans-serif" font-size="11" font-style="italic" fill="#94a3b8" text-anchor="middle">Differential Equations."</text> <!-- Right Panel: Separation of Variables (Process) --> <rect x="600" y="110" width="260" height="340" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="140" font-family="Arial, sans-serif" font-size="18" font-weight="bold" fill="#e879f9">Analytical Engine</text> <text x="620" y="160" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Method: Separation of Variables</text> <g transform="translate(620, 185)"> <circle cx="12" cy="12" r="12" fill="#e879f9"/> <text x="12" y="16" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#0f172a" text-anchor="middle">1</text> <text x="35" y="16" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">SEPARATE</text> <text x="35" y="32" font-family="serif" font-size="12" fill="#94a3b8">g(y) dy = h(x) dx</text> <g transform="translate(0, 50)"> <circle cx="12" cy="12" r="12" fill="#e879f9"/> <text x="12" y="16" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#0f172a" text-anchor="middle">2</text> <text x="35" y="16" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">INTEGRATE</text> <text x="35" y="32" font-family="serif" font-size="12" fill="#94a3b8">∫ g(y) dy = ∫ h(x) dx</text> </g> <g transform="translate(0, 100)"> <circle cx="12" cy="12" r="12" fill="#e879f9"/> <text x="12" y="16" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#0f172a" text-anchor="middle">3</text> <text x="35" y="16" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">SOLVE FOR Y</text> <text x="35" y="32" font-family="serif" font-size="12" fill="#94a3b8">Isolate the dependent variable</text> </g> <g transform="translate(0, 150)"> <circle cx="12" cy="12" r="12" fill="#e879f9"/> <text x="12" y="16" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#0f172a" text-anchor="middle">4</text> <text x="35" y="16" font-family="Arial, sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">APPLY C</text> <text x="35" y="32" font-family="serif" font-size="12" fill="#94a3b8">Use initial condition for C</text> </g> </g> <!-- Bottom Comparison: General vs Particular Curves --> <g transform="translate(40, 470)"> <text x="0" y="20" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">The Solution Spectrum</text> <line x1="0" y1="30" x2="820" y2="30" stroke="#ffffff15" stroke-width="1"/> <!-- Family of curves visualization --> <g transform="translate(600, -10)"> <path d="M 0,40 Q 50,0 100,40" fill="none" stroke="#94a3b8" stroke-width="1" opacity="0.3"/> <path d="M 0,50 Q 50,10 100,50" fill="none" stroke="#94a3b8" stroke-width="1" opacity="0.3"/> <path d="M 0,60 Q 50,20 100,60" fill="none" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <path d="M 0,70 Q 50,30 100,70" fill="none" stroke="#94a3b8" stroke-width="1" opacity="0.3"/> <circle cx="50" cy="20" r="4" fill="#f59e0b"/> <text x="110" y="45" font-family="Arial, sans-serif" font-size="10" fill="#94a3b8">General (Family)</text> <text x="110" y="25" font-family="Arial, sans-serif" font-size="10" fill="#f59e0b" font-weight="bold">Particular (Unique)</text> </g> <text x="0" y="55" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8"> The Existence and Uniqueness Theorem guarantees a single path through any given point in a continuous field. </text> </g> <!-- Decorative Corner Elements --> <path d="M 860 520 L 880 520 L 880 540" fill="none" stroke="#38bdf8" stroke-width="2"/> <path d="M 40 520 L 20 520 L 20 540" fill="none" stroke="#38bdf8" stroke-width="2"/> </svg>Differential Equations and Modeling image 1Differential Equations and Modeling - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/differential-equations/svg/1Differential Equations and Modeling diagram 1Differential Equations and Modeling - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/differential-equations/svg/2Differential Equations and Modeling diagram 2Differential Equations and Modeling - AP/College Calculus AB - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <!-- Decorative Grid --> <g stroke="#ffffff08" stroke-width="1"> <path d="M 0 40 H 900 M 0 80 H 900 M 0 120 H 900 M 0 160 H 900 M 0 200 H 900 M 0 240 H 900 M 0 280 H 900 M 0 320 H 900 M 0 360 H 900 M 0 400 H 900 M 0 440 H 900 M 0 480 H 900 M 0 520 H 900"/> <path d="M 40 0 V 560 M 80 0 V 560 M 120 0 V 560 M 160 0 V 560 M 200 0 V 560 M 240 0 V 560 M 280 0 V 560 M 320 0 V 560 M 360 0 V 560 M 400 0 V 560 M 440 0 V 560 M 480 0 V 560 M 520 0 V 560 M 560 0 V 560 M 600 0 V 560 M 640 0 V 560 M 680 0 V 560 M 720 0 V 560 M 760 0 V 560 M 800 0 V 560 M 840 0 V 560"/> </g> <!-- Header Section --> <text x="40" y="50" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-1">APPLICATIONS OF INTEGRATION</text> <text x="40" y="72" font-family="sans-serif" font-size="14" fill="#94a3b8" font-weight="400">THE CALCULUS OF ACCUMULATION: FROM 1D RATES TO 3D VOLUMES</text> <rect x="520" y="35" width="340" height="2" fill="url(#accentGrad)"/> <!-- Card 1: Net Change --> <rect x="40" y="100" width="400" height="200" rx="16" fill="#ffffff0d" stroke="#ffffff1a"/> <text x="60" y="130" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">01. Net Change &amp; Physics</text> <text x="60" y="150" font-family="sans-serif" font-size="12" fill="#94a3b8">Integrating rates of change to find total accumulation.</text> <!-- Net Change Illustration --> <g transform="translate(60, 170)"> <path d="M 0 80 H 180" stroke="#ffffff40" stroke-width="1"/> <path d="M 0 80 Q 45 10, 90 80 T 180 80" fill="none" stroke="#e879f9" stroke-width="2"/> <path d="M 0 80 Q 45 10, 90 80 L 0 80 Z" fill="#38bdf833"/> <path d="M 90 80 Q 135 150, 180 80 L 90 80 Z" fill="#f43f5e33"/> <text x="200" y="20" font-family="serif" font-style="italic" font-size="14" fill="#f8fafc">∫ v(t) dt = s(b) - s(a)</text> <text x="200" y="45" font-family="sans-serif" font-size="11" fill="#94a3b8">Displacement: Net area</text> <text x="200" y="65" font-family="sans-serif" font-size="11" fill="#94a3b8">Total Distance: ∫ |v(t)| dt</text> </g> <!-- Card 2: Average Value --> <rect x="40" y="320" width="400" height="200" rx="16" fill="#ffffff0d" stroke="#ffffff1a"/> <text x="60" y="350" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">02. Average Value</text> <text x="60" y="370" font-family="sans-serif" font-size="12" fill="#94a3b8">The height of a rectangle with equivalent area.</text> <!-- Average Value Illustration --> <g transform="translate(60, 390)"> <path d="M 0 90 Q 40 20, 100 60 T 180 30" fill="none" stroke="#f59e0b" stroke-width="2"/> <rect x="0" y="55" width="180" height="35" fill="#f59e0b22" stroke="#f59e0b" stroke-dasharray="4"/> <text x="200" y="30" font-family="serif" font-style="italic" font-size="14" fill="#f8fafc">f_avg = [1/(b-a)] ∫ f(x) dx</text> <text x="200" y="55" font-family="sans-serif" font-size="11" fill="#94a3b8">Mean Value Theorem:</text> <text x="200" y="70" font-family="sans-serif" font-size="11" fill="#94a3b8">Guarantees f(c) = f_avg</text> </g> <!-- Card 3: Area Between Curves --> <rect x="460" y="100" width="400" height="240" rx="16" fill="#ffffff0d" stroke="#ffffff1a"/> <text x="480" y="130" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">03. Area Between Curves</text> <!-- Slicing Comparison --> <g transform="translate(480, 150)"> <!-- Vertical Slice --> <path d="M 0 100 Q 50 10, 100 100" fill="none" stroke="#38bdf8" stroke-width="2"/> <path d="M 0 100 Q 50 150, 100 100" fill="none" stroke="#e879f9" stroke-width="2"/> <rect x="45" y="45" width="10" height="85" fill="#ffffff33" stroke="#ffffff"/> <text x="10" y="140" font-family="sans-serif" font-size="11" fill="#f8fafc">Vertical (dx)</text> <text x="10" y="155" font-family="sans-serif" font-size="10" fill="#94a3b8">Top - Bottom</text> <!-- Horizontal Slice --> <g transform="translate(150, 0)"> <path d="M 20 10 Q 110 50, 20 100" fill="none" stroke="#38bdf8" stroke-width="2"/> <path d="M 60 10 Q -30 50, 60 100" fill="none" stroke="#e879f9" stroke-width="2"/> <rect x="25" y="45" width="55" height="10" fill="#ffffff33" stroke="#ffffff"/> <text x="10" y="140" font-family="sans-serif" font-size="11" fill="#f8fafc">Horizontal (dy)</text> <text x="10" y="155" font-family="sans-serif" font-size="10" fill="#94a3b8">Right - Left</text> </g> <text x="0" y="175" font-family="serif" font-style="italic" font-size="13" fill="#f8fafc">A = ∫ [f(x) - g(x)] dx</text> </g> <!-- Card 4: Volume Concept --> <rect x="460" y="360" width="400" height="160" rx="16" fill="#ffffff0d" stroke="#ffffff1a"/> <text x="480" y="390" font-family="sans-serif" font-weight="700" font-size="18" fill="#22d3ee">04. Volume by Slicing</text> <g transform="translate(480, 410)"> <!-- 3D Slices --> <ellipse cx="40" cy="60" rx="30" ry="10" fill="none" stroke="#94a3b8" stroke-dasharray="2"/> <ellipse cx="60" cy="55" rx="35" ry="12" fill="none" stroke="#94a3b8" stroke-dasharray="2"/> <ellipse cx="85" cy="50" rx="40" ry="15" fill="#38bdf844" stroke="#38bdf8" stroke-width="2"/> <ellipse cx="115" cy="45" rx="45" ry="18" fill="none" stroke="#94a3b8" stroke-dasharray="2"/> <text x="180" y="40" font-family="serif" font-style="italic" font-size="16" fill="#f8fafc">V = ∫ A(x) dx</text> <text x="180" y="65" font-family="sans-serif" font-size="11" fill="#94a3b8">Summing infinitesimal</text> <text x="180" y="80" font-family="sans-serif" font-size="11" fill="#94a3b8">cross-sectional areas.</text> </g> <!-- Bottom Label --> <text x="450" y="545" font-family="sans-serif" font-size="10" fill="#475569" text-anchor="middle" letter-spacing="2">CALCULUS II • APPLICATIONS OF THE DEFINITE INTEGRAL • WIKI EDUCATIONAL SERIES</text> <!-- Decorative Elements --> <circle cx="860" cy="40" r="4" fill="#f59e0b"/> <circle cx="840" cy="40" r="4" fill="#e879f9"/> <circle cx="820" cy="40" r="4" fill="#38bdf8"/> </svg>Applications of Integration: Area and Volume image 1Applications of Integration: Area and Volume - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/applications-of-integration/svg/1Applications of Integration: Area and Volume diagram 1Applications of Integration: Area and Volume - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/applications-of-integration/svg/2Applications of Integration: Area and Volume diagram 2Applications of Integration: Area and Volume - AP/College Calculus AB - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header --> <text x="40" y="60" font-family="sans-serif" font-size="32" font-weight="bold" fill="#f8fafc">AP Calculus AB Exam Mastery</text> <text x="40" y="85" font-family="sans-serif" font-size="16" fill="#94a3b8">A Comprehensive Guide to Conceptual Synthesis &amp; Problem Solving</text> <line x1="40" y1="105" x2="860" y2="105" stroke="#38bdf8" stroke-width="2" opacity="0.5"/> <!-- Left Column: The Big Four --> <rect x="40" y="130" width="260" height="390" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="60" y="165" font-family="sans-serif" font-size="18" font-weight="bold" fill="#f59e0b">The Core Pillars</text> <!-- Pillar 1 --> <circle cx="80" cy="210" r="20" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <path d="M 75 210 L 85 210 M 80 205 L 80 215" stroke="#38bdf8" stroke-width="2"/> <text x="110" y="205" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Limits &amp; Continuity</text> <text x="110" y="222" font-family="sans-serif" font-size="11" fill="#94a3b8">The foundation of local behavior.</text> <!-- Pillar 2 --> <circle cx="80" cy="280" r="20" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <line x1="70" y1="290" x2="90" y2="270" stroke="#e879f9" stroke-width="2"/> <text x="110" y="275" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Differentiation</text> <text x="110" y="292" font-family="sans-serif" font-size="11" fill="#94a3b8">Rates of change &amp; tangent slopes.</text> <!-- Pillar 3 --> <circle cx="80" cy="350" r="20" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2"/> <path d="M 75 360 Q 80 350 85 340" stroke="#f59e0b" stroke-width="2" fill="none"/> <text x="110" y="345" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Integration</text> <text x="110" y="362" font-family="sans-serif" font-size="11" fill="#94a3b8">Accumulation &amp; area under curves.</text> <!-- Pillar 4 --> <circle cx="80" cy="420" r="20" fill="#10b98120" stroke="#10b981" stroke-width="2"/> <path d="M 72 420 L 88 420 M 80 412 L 80 428" stroke="#10b981" stroke-width="1" fill="none" transform="rotate(45 80 420)"/> <text x="110" y="415" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">Differential Eq.</text> <text x="110" y="432" font-family="sans-serif" font-size="11" fill="#94a3b8">Modeling growth and separation.</text> <!-- Right Top: FRQ Architecture --> <rect x="320" y="130" width="540" height="160" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="340" y="165" font-family="sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">FRQ Architecture (50% of Score)</text> <!-- Part A --> <rect x="340" y="185" width="240" height="80" rx="12" fill="#38bdf810"/> <text x="355" y="210" font-family="sans-serif" font-size="14" font-weight="bold" fill="#38bdf8">Part A: Questions 1–2</text> <text x="355" y="230" font-family="sans-serif" font-size="12" fill="#f8fafc">Graphing Calculator Required</text> <text x="355" y="248" font-family="sans-serif" font-size="11" fill="#94a3b8">Focus: Complex functions, Rate In/Out</text> <!-- Part B --> <rect x="600" y="185" width="240" height="80" rx="12" fill="#e879f910"/> <text x="615" y="210" font-family="sans-serif" font-size="14" font-weight="bold" fill="#e879f9">Part B: Questions 3–6</text> <text x="615" y="230" font-family="sans-serif" font-size="12" fill="#f8fafc">No Calculator Permitted</text> <text x="615" y="248" font-family="sans-serif" font-size="11" fill="#94a3b8">Focus: Theorems, Graphs, Tables</text> <!-- Right Bottom: Scoring Rubric Path --> <rect x="320" y="310" width="540" height="210" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="340" y="345" font-family="sans-serif" font-size="18" font-weight="bold" fill="#e879f9">The "Point-Stacking" Rubric</text> <!-- Step 1 --> <rect x="340" y="365" width="110" height="130" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <text x="395" y="390" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc" text-anchor="middle">1. SETUP</text> <text x="395" y="415" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">Write the integral</text> <text x="395" y="430" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">or derivative.</text> <text x="395" y="460" font-family="sans-serif" font-size="10" fill="#38bdf8" text-anchor="middle" font-style="italic">Don't forget dx!</text> <!-- Step 2 --> <rect x="465" y="365" width="110" height="130" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <text x="520" y="390" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc" text-anchor="middle">2. CALC</text> <text x="520" y="415" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">Apply rules:</text> <text x="520" y="430" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">Chain, Power, FTC.</text> <text x="520" y="460" font-family="sans-serif" font-size="10" fill="#38bdf8" text-anchor="middle" font-style="italic">Show your steps.</text> <!-- Step 3 --> <rect x="590" y="365" width="110" height="130" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <text x="645" y="390" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc" text-anchor="middle">3. JUSTIFY</text> <text x="645" y="415" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">Name the theorem:</text> <text x="645" y="430" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">MVT, IVT, EVT.</text> <text x="645" y="460" font-family="sans-serif" font-size="10" fill="#38bdf8" text-anchor="middle" font-style="italic">Avoid using "it".</text> <!-- Step 4 --> <rect x="715" y="365" width="110" height="130" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <text x="770" y="390" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc" text-anchor="middle">4. UNITS</text> <text x="770" y="415" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">Final answer with</text> <text x="770" y="430" font-family="sans-serif" font-size="11" fill="#94a3b8" text-anchor="middle">correct units.</text> <text x="770" y="460" font-family="sans-serif" font-size="10" fill="#38bdf8" text-anchor="middle" font-style="italic">e.g. ft/sec²</text> <!-- Connectors --> <path d="M 450 430 L 465 430" stroke="#ffffff20" stroke-width="2" marker-end="url(#arrow)"/> <path d="M 575 430 L 590 430" stroke="#ffffff20" stroke-width="2"/> <path d="M 700 430 L 715 430" stroke="#ffffff20" stroke-width="2"/> <!-- Decorative FTC Formula --> <g opacity="0.4" transform="translate(680, 40)"> <rect x="0" y="0" width="180" height="45" rx="8" fill="#38bdf810" stroke="#38bdf8" stroke-dasharray="4"/> <text x="90" y="28" font-family="serif" font-size="14" fill="#38bdf8" text-anchor="middle" font-style="italic">∫ f'(x) dx = f(b) - f(a)</text> </g> </svg>AP Calculus AB Exam Preparation image 1AP Calculus AB Exam Preparation - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/ap-exam-prep/svg/1AP Calculus AB Exam Preparation diagram 1AP Calculus AB Exam Preparation - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/ap-exam-prep/svg/2AP Calculus AB Exam Preparation diagram 2AP Calculus AB Exam Preparation - AP/College Calculus AB - diagram 2https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/ap-exam-prep/svg/3AP Calculus AB Exam Preparation diagram 3AP Calculus AB Exam Preparation - AP/College Calculus AB - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">COURSE CHALLENGE &amp; MASTERY</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">The Terminal Phase of the AP Calculus AB Pedagogical Lifecycle</text> <line x1="350" y1="90" x2="550" y2="90" stroke="url(#accentGrad)" stroke-width="2" stroke-linecap="round"/> <!-- Left Column: Mastery Progression --> <rect x="40" y="110" width="260" height="280" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">The Mastery Ladder</text> <!-- Progression Steps --> <g transform="translate(60, 170)"> <!-- Mastered --> <circle cx="15" cy="0" r="12" fill="#f59e0b" filter="url(#glow)"/> <text x="40" y="5" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">MASTERED</text> <text x="40" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">Course Challenge Success</text> <line x1="15" y1="12" x2="15" y2="38" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4 2"/> <!-- Proficient --> <circle cx="15" cy="50" r="10" fill="#e879f9"/> <text x="40" y="55" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Proficient</text> <text x="40" y="70" font-family="sans-serif" font-size="11" fill="#94a3b8">Unit Test Consistency</text> <line x1="15" y1="60" x2="15" y2="88" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4 2"/> <!-- Familiar --> <circle cx="15" cy="100" r="10" fill="#38bdf8"/> <text x="40" y="105" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Familiar</text> <text x="40" y="120" font-family="sans-serif" font-size="11" fill="#94a3b8">Quiz Performance</text> <line x1="15" y1="110" x2="15" y2="138" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4 2"/> <!-- Attempted --> <circle cx="15" cy="150" r="10" fill="#64748b"/> <text x="40" y="155" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Attempted</text> <text x="40" y="170" font-family="sans-serif" font-size="11" fill="#94a3b8">Initial Engagement</text> </g> <!-- Center: The 30-Question Gauntlet --> <rect x="320" y="110" width="540" height="280" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="340" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">The 30-Question Gauntlet</text> <!-- Gauntlet Visualization --> <g transform="translate(430, 250)"> <!-- Central Core --> <circle r="45" fill="none" stroke="url(#accentGrad)" stroke-width="2" stroke-dasharray="5 3"/> <text text-anchor="middle" y="5" font-family="sans-serif" font-weight="800" font-size="12" fill="#f8fafc">CUMULATIVE</text> <!-- Radiating Skill Nodes --> <path d="M 0,-45 L 0,-80" stroke="#38bdf8" stroke-width="2"/> <path d="M 39,-22 L 70,-40" stroke="#38bdf8" stroke-width="2"/> <path d="M 39,22 L 70,40" stroke="#38bdf8" stroke-width="2"/> <path d="M 0,45 L 0,80" stroke="#38bdf8" stroke-width="2"/> <path d="M -39,22 L -70,40" stroke="#38bdf8" stroke-width="2"/> <path d="M -39,-22 L -70,-40" stroke="#38bdf8" stroke-width="2"/> <!-- Small Question Dots --> <circle cx="0" cy="-85" r="4" fill="#f59e0b"/> <circle cx="75" cy="-45" r="4" fill="#f59e0b"/> <circle cx="75" cy="45" r="4" fill="#f59e0b"/> <circle cx="0" cy="85" r="4" fill="#f59e0b"/> <circle cx="-75" cy="45" r="4" fill="#f59e0b"/> <circle cx="-75" cy="-45" r="4" fill="#f59e0b"/> </g> <!-- Mastery Coefficient Formula Box --> <g transform="translate(580, 160)"> <rect width="250" height="100" rx="12" fill="#00000030" stroke="#ffffff10"/> <text x="125" y="30" text-anchor="middle" font-family="serif" font-size="16" fill="#f8fafc" font-style="italic">The Mastery Coefficient (ℳ)</text> <text x="125" y="65" text-anchor="middle" font-family="serif" font-size="20" fill="#f59e0b">ℳ = ∫₀ᵀ [a(t)·d(t) / e⁻λᵗ] dt</text> <text x="125" y="85" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">Accuracy × Difficulty / Forgetting Curve</text> </g> <!-- Bottom: Comparison Tiers --> <text x="40" y="425" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">Assessment Tier Comparison</text> <!-- Tier 1: Quiz --> <rect x="40" y="440" width="260" height="90" rx="12" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="465" font-family="sans-serif" font-weight="700" font-size="14" fill="#38bdf8">QUIZ</text> <text x="60" y="485" font-family="sans-serif" font-size="12" fill="#f8fafc">Scope: 2-3 Skills</text> <text x="60" y="505" font-family="sans-serif" font-size="12" fill="#94a3b8">Context Switching: Low</text> <text x="60" y="520" font-family="sans-serif" font-size="11" fill="#38bdf8">Ceiling: Proficient</text> <!-- Tier 2: Unit Test --> <rect x="320" y="440" width="260" height="90" rx="12" fill="#ffffff0a" stroke="#ffffff15"/> <text x="340" y="465" font-family="sans-serif" font-weight="700" font-size="14" fill="#e879f9">UNIT TEST</text> <text x="340" y="485" font-family="sans-serif" font-size="12" fill="#f8fafc">Scope: Single Unit (U1-10)</text> <text x="340" y="505" font-family="sans-serif" font-size="12" fill="#94a3b8">Context Switching: Moderate</text> <text x="340" y="520" font-family="sans-serif" font-size="11" fill="#e879f9">Ceiling: Proficient</text> <!-- Tier 3: Course Challenge --> <rect x="600" y="440" width="260" height="90" rx="12" fill="#f59e0b15" stroke="#f59e0b40"/> <text x="620" y="465" font-family="sans-serif" font-weight="700" font-size="14" fill="#f59e0b">COURSE CHALLENGE</text> <text x="620" y="485" font-family="sans-serif" font-size="12" fill="#f8fafc">Scope: Entire Curriculum</text> <text x="620" y="505" font-family="sans-serif" font-size="12" fill="#94a3b8">Context Switching: Extreme</text> <text x="620" y="520" font-family="sans-serif" font-weight="700" font-size="11" fill="#f59e0b">Ceiling: MASTERED</text> <!-- Decorative Corner Elements --> <circle cx="880" cy="20" r="40" fill="#38bdf808"/> <circle cx="20" cy="540" r="60" fill="#e879f908"/> </svg>Course Challenge and Mastery image 1Course Challenge and Mastery - AP/College Calculus AB - image 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/course-challenge/svg/1Course Challenge and Mastery diagram 1Course Challenge and Mastery - AP/College Calculus AB - diagram 1https://www.getlykke.com/explore/public/apcollege-calculus-ab-32566f4a-f483-4cb5-98bd-98e5a44b121c/media/course-challenge/svg/2Course Challenge and Mastery diagram 2Course Challenge and Mastery - AP/College Calculus AB - diagram 2https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e262026-04-20T04:57:55.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="30" height="30" patternUnits="userSpaceOnUse"> <circle cx="1" cy="1" r="1" fill="#ffffff10" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">FUNCTIONS &amp; LINEAR MODELING</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="2">THE ARCHITECTURE OF MATHEMATICAL RELATIONSHIPS</text> <line x1="350" y1="85" x2="550" y2="85" stroke="#38bdf8" stroke-width="2" stroke-linecap="round"/> <!-- Card 1: The Mapping Paradigm --> <rect x="40" y="110" width="260" height="200" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">THE MAPPING PARADIGM</text> <text x="60" y="165" font-family="sans-serif" font-size="12" fill="#94a3b8">A function is a rule where every</text> <text x="60" y="180" font-family="sans-serif" font-size="12" fill="#94a3b8">input has exactly ONE output.</text> <!-- Mapping Visual --> <circle cx="85" cy="235" r="25" fill="#38bdf820" stroke="#38bdf8" stroke-width="1.5"/> <text x="85" y="240" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#38bdf8">D</text> <circle cx="215" cy="235" r="25" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1.5"/> <text x="215" y="240" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f59e0b">R</text> <path d="M115 235 L185 235" stroke="#f8fafc" stroke-width="2" marker-end="url(#arrowhead)"/> <path d="M115 220 Q150 200 185 220" stroke="#f8fafc" stroke-width="1" stroke-dasharray="4"/> <path d="M115 250 Q150 270 185 250" stroke="#f8fafc" stroke-width="1" stroke-dasharray="4"/> <text x="150" y="215" text-anchor="middle" font-family="serif" font-style="italic" font-size="16" fill="#e879f9">f</text> <!-- Card 2: The Function Machine --> <rect x="320" y="110" width="260" height="200" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="340" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">FUNCTION NOTATION</text> <!-- Machine Visual --> <rect x="390" y="180" width="120" height="80" rx="8" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="450" y="225" text-anchor="middle" font-family="serif" font-size="24" font-weight="bold" fill="#e879f9">f(x)</text> <path d="M340 220 L390 220" stroke="#38bdf8" stroke-width="3" marker-end="url(#arrowhead)"/> <text x="355" y="210" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#38bdf8">INPUT</text> <path d="M510 220 L560 220" stroke="#f59e0b" stroke-width="3" marker-end="url(#arrowhead)"/> <text x="545" y="210" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f59e0b">OUTPUT</text> <text x="450" y="285" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#94a3b8">"Value of f at input x"</text> <!-- Card 3: Domain & Range --> <rect x="600" y="110" width="260" height="200" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">CONSTRAINTS</text> <text x="620" y="170" font-family="sans-serif" font-size="13" font-weight="bold" fill="#38bdf8">DOMAIN (Inputs)</text> <text x="620" y="188" font-family="sans-serif" font-size="11" fill="#94a3b8">• No division by zero</text> <text x="620" y="204" font-family="sans-serif" font-size="11" fill="#94a3b8">• No even roots of negatives</text> <text x="620" y="235" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f59e0b">RANGE (Outputs)</text> <text x="620" y="253" font-family="sans-serif" font-size="11" fill="#94a3b8">• The set of all resulting values</text> <text x="620" y="269" font-family="sans-serif" font-size="11" fill="#94a3b8">• Interval Notation: [min, max]</text> <!-- Bottom Card: Visual Analysis & Linear Modeling --> <rect x="40" y="330" width="820" height="200" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <!-- VLT 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FUNCTION.</text> </g> <!-- Linear Modeling Section --> <line x1="410" y1="350" x2="410" y2="510" stroke="#ffffff15" stroke-width="1"/> <text x="440" y="365" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">LINEAR MODELING</text> <text x="440" y="390" font-family="serif" font-size="22" fill="#38bdf8" font-weight="bold">f(x) = mx + b</text> <g transform="translate(440, 410)"> <rect width="380" height="90" rx="8" fill="#ffffff05"/> <text x="15" y="25" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f59e0b">m = Slope (Rate of Change)</text> <text x="15" y="42" font-family="sans-serif" font-size="11" fill="#94a3b8">The constant propagation of change: Δy / Δx</text> <text x="15" y="65" font-family="sans-serif" font-size="13" font-weight="bold" fill="#e879f9">b = y-intercept (Initial Value)</text> <text x="15" y="82" font-family="sans-serif" font-size="11" fill="#94a3b8">The starting state of the system where x = 0</text> <!-- Slope Triangle Visual --> <g transform="translate(280, 10)"> <line x1="0" y1="60" x2="60" y2="10" stroke="#38bdf8" stroke-width="2"/> <path d="M20 43 L50 43 L50 18" fill="none" stroke="#f59e0b" stroke-width="1" stroke-dasharray="2"/> <text x="55" y="35" font-family="sans-serif" font-size="9" fill="#f59e0b">Δy</text> <text x="30" y="55" font-family="sans-serif" font-size="9" fill="#f59e0b">Δx</text> </g> </g> <!-- Markers --> <defs> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="#f8fafc" /> </marker> </defs> </svg>Functions and Linear Modeling image 1Functions and Linear Modeling - Precalculus 2e - image 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/functions-and-linear-modeling/svg/1Functions and Linear Modeling diagram 1Functions and Linear Modeling - Precalculus 2e - diagram 1<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" 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stroke="url(#accentGrad)" stroke-width="2" stroke-linecap="round" opacity="0.6"/> <text x="450" y="95" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-weight="300">From Smooth Curvature to Asymptotic Boundaries</text> <!-- Left Card: Polynomials --> <rect x="40" y="130" width="400" height="260" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="75" cy="165" r="18" fill="#38bdf820"/> <path d="M 65 170 Q 75 150 85 170" fill="none" stroke="#38bdf8" stroke-width="2.5"/> <text x="105" y="170" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">Polynomial Functions</text> <!-- Mini Graph: Parabola --> <g transform="translate(70, 200)"> <line x1="0" y1="60" x2="120" y2="60" stroke="#94a3b8" stroke-width="1" opacity="0.5"/> <line x1="60" y1="0" x2="60" y2="100" stroke="#94a3b8" stroke-width="1" opacity="0.5"/> <path d="M 20 10 Q 60 110 100 10" fill="none" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <circle cx="60" cy="60" r="4" fill="#f8fafc"/> <text x="65" y="55" font-family="sans-serif" font-size="10" fill="#f8fafc">Vertex (h, k)</text> </g> <g transform="translate(210, 210)"> <text x="0" y="0" font-family="sans-serif" font-size="13" font-weight="600" fill="#38bdf8">QUADRATIC OPTIMIZATION</text> <text x="0" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">f(x) = a(x - h)² + k</text> <text x="0" y="45" font-family="sans-serif" font-size="11" fill="#cbd5e1" width="180"> <tspan x="0" dy="0">• Vertex is the absolute extreme</tspan> <tspan x="0" dy="18">• h = -b / 2a (Standard Form)</tspan> <tspan x="0" dy="18">• Models acceleration &amp; range</tspan> </text> </g> <!-- Right Card: Rational --> <rect x="460" y="130" width="400" height="260" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <circle cx="495" cy="165" r="18" fill="#e879f920"/> <path d="M 485 175 L 505 155 M 485 155 L 505 175" fill="none" stroke="#e879f9" stroke-width="2.5"/> <text x="525" y="170" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">Rational Functions</text> <!-- Mini Graph: Rational --> <g transform="translate(490, 200)"> <line x1="0" y1="50" x2="120" y2="50" stroke="#94a3b8" stroke-width="1" opacity="0.5"/> <line x1="60" y1="0" x2="60" y2="100" stroke="#94a3b8" stroke-width="1" opacity="0.5"/> <!-- Asymptote --> <line x1="60" y1="0" x2="60" y2="100" stroke="#e879f9" stroke-width="1" stroke-dasharray="4 2"/> <path d="M 10 45 Q 50 45 55 5 M 65 95 Q 70 55 110 55" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <text x="65" y="15" font-family="sans-serif" font-size="10" fill="#e879f9">Asymptote</text> </g> <g transform="translate(630, 210)"> <text x="0" y="0" font-family="sans-serif" font-size="13" font-weight="600" fill="#e879f9">LIMIT BEHAVIOR</text> <text x="0" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">f(x) = P(x) / Q(x)</text> <text x="0" y="45" font-family="sans-serif" font-size="11" fill="#cbd5e1"> <tspan x="0" dy="0">• 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font-family="monospace" font-size="14" fill="#f8fafc">c | aₙ aₙ₋₁ ... a₀</text> <path d="M -5 22 L 130 22" stroke="#38bdf8" stroke-width="1"/> <text x="15" y="40" font-family="monospace" font-size="14" fill="#94a3b8">qₙ₋₁ qₙ₋₂ ... r</text> </g> </g> <line x1="580" y1="430" x2="580" y2="510" stroke="#ffffff10" stroke-width="1"/> <g transform="translate(610, 445)"> <text x="0" y="0" font-family="sans-serif" font-weight="700" font-size="14" fill="#e879f9">FACTOR THEOREM</text> <text x="0" y="22" font-family="sans-serif" font-size="12" fill="#94a3b8">(x - c) is a factor if and</text> <text x="0" y="40" font-family="sans-serif" font-size="12" fill="#f8fafc" font-weight="600">only if f(c) = 0.</text> </g> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="url(#accentGrad)" opacity="0.1"/> <circle cx="50" cy="510" r="20" fill="#f59e0b" opacity="0.1"/> </svg>Polynomial and Rational Functions image 1Polynomial and Rational Functions - Precalculus 2e - image 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/polynomial-and-rational-functions/svg/1Polynomial and Rational Functions diagram 1Polynomial and Rational Functions - Precalculus 2e - diagram 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/polynomial-and-rational-functions/svg/2Polynomial and Rational Functions diagram 2Polynomial and Rational Functions - Precalculus 2e - diagram 2https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/polynomial-and-rational-functions/svg/3Polynomial and Rational Functions diagram 3Polynomial and Rational Functions - Precalculus 2e - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" 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text-transform="uppercase" letter-spacing="0.1em">The Mathematics of Multiplicative Change</text> <!-- Left Panel: Exponential Growth --> <rect x="40" y="130" width="260" height="320" rx="20" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="65" y="165" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#f59e0b">Exponential Growth</text> <text x="65" y="190" font-family="serif" font-style="italic" font-size="16" fill="#f8fafc">f(x) = a · bˣ</text> <path d="M 70 340 Q 180 340 260 220" fill="none" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <circle cx="70" cy="340" r="4" fill="#f59e0b"/> <text x="65" y="370" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8">Constant Ratio Property:</text> <text x="65" y="388" font-family="system-ui, sans-serif" font-size="12" fill="#f8fafc">Outputs grow by a factor of 'b'</text> <text x="65" y="405" font-family="system-ui, sans-serif" font-size="12" fill="#f8fafc">for every unit increase in 'x'.</text> <!-- Right Panel: Logarithmic Functions --> <rect x="600" y="130" width="260" height="320" rx="20" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="625" y="165" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#38bdf8">Logarithmic Scale</text> <text x="625" y="190" font-family="serif" font-style="italic" font-size="16" fill="#f8fafc">f(x) = log_b(x)</text> <path d="M 630 220 Q 630 340 780 340" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <circle cx="780" cy="340" r="4" fill="#38bdf8"/> <text x="625" y="370" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8">The Inverse Operation:</text> <text x="625" y="388" font-family="system-ui, sans-serif" font-size="12" fill="#f8fafc">Logs answer: "To what power</text> <text x="625" y="405" font-family="system-ui, sans-serif" font-size="12" fill="#f8fafc">must we raise b to get x?"</text> <!-- Center Hub: The Natural Base e --> <circle cx="450" y="280" r="85" fill="#1e1b4b" stroke="#e879f9" stroke-width="2" stroke-dasharray="8 4"/> <text x="450" y="285" text-anchor="middle" font-family="serif" font-style="italic" font-weight="800" font-size="72" fill="#e879f9" filter="url(#glow)">e</text> <text x="450" y="320" text-anchor="middle" font-family="system-ui, sans-serif" font-size="14" font-weight="bold" fill="#f8fafc">≈ 2.71828</text> <text x="450" y="180" text-anchor="middle" font-family="system-ui, sans-serif" font-size="13" fill="#94a3b8">The Natural Base</text> <!-- Connecting Arrows (Inverse Relationship) --> <path d="M 320 280 L 355 280" stroke="#e879f9" stroke-width="2" marker-end="url(#arrow)"/> <path d="M 545 280 L 580 280" stroke="#e879f9" stroke-width="2" marker-start="url(#arrow)"/> <!-- Application Icons (Bottom Row) --> <g transform="translate(150, 480)"> <circle cx="0" cy="0" r="25" fill="#ffffff10"/> <text x="0" y="5" text-anchor="middle" font-size="20" fill="#f59e0b">$</text> <text x="0" y="45" text-anchor="middle" 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y="45" text-anchor="middle" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Information</text> </g> <!-- Definitions for Markers --> <defs> <marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="4" markerHeight="4" orient="auto-start-reverse"> <path d="M 0 0 L 10 5 L 0 10 z" fill="#e879f9" /> </marker> </defs> <!-- Decorative labels --> <text x="450" y="400" text-anchor="middle" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8" font-style="italic">"The bridge between addition and multiplication"</text> </svg>Exponential and Logarithmic Functions image 1Exponential and Logarithmic Functions - Precalculus 2e - image 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/exponential-and-logarithmic-functions/svg/1Exponential and Logarithmic Functions diagram 1Exponential and Logarithmic Functions - Precalculus 2e - diagram 1<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">TRIGONOMETRY &amp; PERIODIC FUNCTIONS</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">Bridging Static Geometry and Dynamic Oscillations</text> <!-- Left Panel: The Unit Circle --> <rect x="40" y="100" width="380" height="320" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="135" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">The Unit Circle (r = 1)</text> <!-- Circle Diagram --> <circle cx="210" cy="260" r="80" fill="none" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4 2"/> <line x1="110" y1="260" x2="310" y2="260" stroke="#ffffff33" stroke-width="1"/> <line x1="210" y1="160" x2="210" y2="360" stroke="#ffffff33" stroke-width="1"/> <!-- Angle and Point --> <path d="M 210 260 L 266.5 203.5" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <circle cx="266.5" cy="203.5" r="4" fill="#f59e0b"/> <text x="275" y="195" font-family="sans-serif" font-size="12" fill="#f8fafc">P(x, y)</text> <!-- Trig Labels --> <line x1="266.5" y1="260" x2="266.5" y2="203.5" stroke="#e879f9" stroke-width="2" stroke-dasharray="2 2"/> <text x="272" y="240" font-family="sans-serif" font-size="11" fill="#e879f9">sin(θ) = y</text> <line x1="210" y1="260" x2="266.5" y2="260" stroke="#38bdf8" stroke-width="2"/> <text x="220" y="275" font-family="sans-serif" font-size="11" fill="#38bdf8">cos(θ) = x</text> <!-- Radians/Degrees Box --> <rect x="60" y="350" width="340" height="50" rx="8" fill="#00000033"/> <text x="75" y="372" font-family="sans-serif" font-size="11" font-weight="bold" fill="#94a3b8">CONVERSION</text> <text x="75" y="388" font-family="sans-serif" font-size="13" fill="#f8fafc">180° = π rad</text> <text x="200" y="388" font-family="sans-serif" font-size="13" fill="#f8fafc">1 rad ≈ 57.3°</text> <text x="310" y="388" font-family="sans-serif" font-size="13" fill="#f8fafc">360° = 2π</text> <!-- Right Panel: Periodic Wave --> <rect x="440" y="100" width="420" height="320" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="460" y="135" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">Periodic Behavior</text> <!-- Wave Graph --> <path d="M 460 260 L 840 260" stroke="#ffffff33" stroke-width="1"/> <path d="M 460 180 L 840 180" stroke="#ffffff11" stroke-width="1" stroke-dasharray="4 4"/> <path d="M 460 340 L 840 340" stroke="#ffffff11" stroke-width="1" stroke-dasharray="4 4"/> <!-- Sine Wave Path --> <path d="M 460 260 C 500 100, 540 100, 580 260 C 620 420, 660 420, 700 260 C 740 100, 780 100, 820 260" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <!-- Wave Annotations --> <path d="M 540 260 L 540 180" stroke="#f59e0b" stroke-width="2" marker-end="url(#arrow)"/> <text x="545" y="220" font-family="sans-serif" font-size="11" fill="#f59e0b">Amplitude (A)</text> <path d="M 460 360 L 700 360" stroke="#38bdf8" stroke-width="1"/> <line x1="460" y1="355" x2="460" y2="365" stroke="#38bdf8" stroke-width="1"/> <line x1="700" y1="355" x2="700" y2="365" stroke="#38bdf8" stroke-width="1"/> <text x="540" y="380" font-family="sans-serif" font-size="11" fill="#38bdf8" text-anchor="middle">Period (P = 2π/|B|)</text> <!-- Formula Card --> <rect x="460" y="145" width="380" height="30" rx="6" fill="#ffffff08"/> <text x="650" y="165" text-anchor="middle" font-family="serif" font-size="16" fill="#f8fafc" font-style="italic">f(x) = A sin(B(x - C)) + D</text> <!-- Bottom Section: Applications & Implementation --> <rect x="40" y="440" width="820" height="90" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <!-- App Icons --> <g transform="translate(70, 465)"> <circle cx="20" cy="20" r="15" fill="#38bdf822" stroke="#38bdf8" stroke-width="1"/> <path d="M 12 20 Q 16 10 20 20 T 28 20" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="45" y="18" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Sound Waves</text> <text x="45" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Acoustics &amp; Music</text> </g> <g transform="translate(240, 465)"> <circle cx="20" cy="20" r="15" fill="#e879f922" stroke="#e879f9" stroke-width="1"/> <circle cx="20" cy="20" r="4" fill="#e879f9"/> <circle cx="32" cy="12" r="3" fill="#f8fafc"/> <text x="45" y="18" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Orbital Mechanics</text> <text x="45" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Celestial Cycles</text> </g> <g transform="translate(450, 465)"> <rect x="0" y="5" width="340" height="60" rx="8" fill="#00000044"/> <text x="10" y="22" font-family="monospace" font-size="10" fill="#38bdf8">sin(x) = x - x³/3! + x⁵/5! - ...</text> <text x="10" y="40" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">Taylor Series Expansion</text> <text x="10" y="54" font-family="sans-serif" font-size="11" fill="#94a3b8">Low-level computational approximation</text> </g> <!-- Connecting Visual --> <path d="M 266.5 203.5 Q 350 150, 460 260" fill="none" stroke="#ffffff22" stroke-width="2" stroke-dasharray="5 5"/> <!-- Decorative Dots --> <circle cx="860" cy="40" r="3" fill="#f59e0b"/> <circle cx="840" cy="40" r="3" fill="#e879f9"/> <circle cx="820" cy="40" r="3" fill="#38bdf8"/> </svg>Trigonometry and Periodic Functions image 1Trigonometry and Periodic Functions - Precalculus 2e - image 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/trigonometry-and-periodic-functions/svg/1Trigonometry and Periodic Functions diagram 1Trigonometry and Periodic Functions - Precalculus 2e - diagram 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/trigonometry-and-periodic-functions/svg/2Trigonometry and Periodic Functions diagram 2Trigonometry and Periodic Functions - Precalculus 2e - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="60" text-anchor="middle" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">ANALYTIC GEOMETRY &amp; THE CALCULUS BRIDGE</text> <text x="450" y="85" text-anchor="middle" font-family="Arial, sans-serif" font-size="16" fill="#94a3b8" font-style="italic">The Transition from Static Relationships to Dynamic Motion</text> <line x1="300" y1="100" x2="600" y2="100" stroke="#38bdf8" stroke-width="2" stroke-dasharray="8 4" opacity="0.5"/> <!-- Left Column: Conic Sections --> <rect x="30" y="120" width="265" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="50" y="155" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">CONIC SECTIONS</text> <text x="50" y="175" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">The Geometry of Quadratic Loci</text> <!-- Cone Illustration --> <path d="M 160 200 L 100 300 L 220 300 Z" fill="none" stroke="#ffffff30" stroke-width="1.5"/> <path d="M 160 400 L 100 300 L 220 300 Z" fill="none" stroke="#ffffff30" stroke-width="1.5"/> <ellipse cx="160" cy="230" rx="25" ry="8" fill="none" stroke="#f59e0b" stroke-width="2" filter="url(#glow)"/> <!-- Circle --> <path d="M 130 250 Q 160 265 190 250" fill="none" stroke="#e879f9" stroke-width="2"/> <!-- Ellipse slice --> <path d="M 115 340 Q 160 310 205 340" fill="none" stroke="#38bdf8" stroke-width="2"/> <!-- Parabola slice --> <text x="50" y="420" font-family="Arial, sans-serif" font-size="11" fill="#f8fafc" font-weight="bold">GENERAL EQUATION:</text> <text x="50" y="438" font-family="serif" font-size="13" fill="#f8fafc">Ax² + Bxy + Cy² + Dx + Ey + F = 0</text> <g font-family="Arial, sans-serif" font-size="11"> <circle cx="55" cy="465" r="4" fill="#f59e0b"/> <text x="68" y="469" fill="#94a3b8">Circle (e = 0)</text> <circle cx="55" cy="482" r="4" fill="#e879f9"/> <text x="68" y="486" fill="#94a3b8">Ellipse (0 ≤ e &lt; 1)</text> <circle cx="165" cy="465" r="4" fill="#38bdf8"/> <text x="178" y="469" fill="#94a3b8">Parabola (e = 1)</text> <circle cx="165" cy="482" r="4" fill="#fb7185"/> <text x="178" y="486" fill="#94a3b8">Hyperbola (e &gt; 1)</text> </g> <!-- Center Column: The Limit --> <rect x="315" y="120" width="270" height="400" rx="16" fill="#ffffff12" stroke="#38bdf840" stroke-width="2"/> <text x="450" y="155" text-anchor="middle" font-family="Arial, sans-serif" font-weight="bold" font-size="20" fill="#f59e0b">THE LIMIT CONCEPT</text> <text x="450" y="175" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Gateway to the Infinitesimal</text> <!-- Limit Visual --> <path d="M 350 350 Q 450 350 550 220" fill="none" stroke="#ffffff20" stroke-width="3"/> <circle cx="480" cy="305" r="5" fill="#f59e0b" filter="url(#glow)"/> <line x1="430" y1="335" x2="530" y2="275" stroke="#38bdf8" stroke-width="2"/> <!-- Tangent --> <text x="450" y="380" text-anchor="middle" font-family="serif" font-size="22" fill="#f8fafc">lim f(x) = L</text> <text x="450" y="400" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">x → c</text> <rect x="340" y="425" width="220" height="75" rx="8" fill="#00000030"/> <text x="355" y="445" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#f59e0b">THE FORMAL DEFINITION</text> <text x="355" y="465" font-family="serif" font-size="12" fill="#cbd5e1">For every ε &gt; 0, there exists a δ &gt; 0</text> <text x="355" y="482" font-family="serif" font-size="12" fill="#cbd5e1">such that |f(x) - L| &lt; ε whenever</text> <text x="355" y="495" font-family="serif" font-size="12" fill="#cbd5e1">0 &lt; |x - c| &lt; δ.</text> <!-- Right Column: Sequences & Series --> <rect x="605" y="120" width="265" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="625" y="155" font-family="Arial, sans-serif" font-weight="bold" font-size="18" fill="#e879f9">SEQUENCES &amp; SERIES</text> <text x="625" y="175" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Discrete Foundations of Sums</text> <!-- Series Visual --> <g transform="translate(640, 220)"> <rect x="0" y="80" width="20" height="20" fill="#e879f9" opacity="1"/> <rect x="25" y="90" width="20" height="10" fill="#e879f9" opacity="0.8"/> <rect x="50" y="95" width="20" height="5" fill="#e879f9" opacity="0.6"/> <rect x="75" y="97" width="20" height="3" fill="#e879f9" opacity="0.4"/> <rect x="100" y="98" width="20" height="2" fill="#e879f9" opacity="0.2"/> <text x="0" y="120" font-family="serif" font-size="14" fill="#f8fafc">Σ arⁿ⁻¹</text> </g> <path d="M 625 340 L 850 340" stroke="#ffffff15" stroke-width="1"/> <text x="625" y="370" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#e879f9">CONVERGENCE CONDITION</text> <text x="625" y="390" font-family="serif" font-size="14" fill="#f8fafc">| r | &lt; 1</text> <text x="625" y="410" font-family="Arial, sans-serif" font-size="11" fill="#94a3b8">If met, the infinite sum is:</text> <text x="625" y="435" font-family="serif" font-size="18" fill="#f8fafc">S = a₁ / (1 - r)</text> <rect x="625" y="455" width="225" height="45" rx="6" fill="#e879f915"/> <text x="635" y="473" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="#f8fafc">THE BINOMIAL THEOREM</text> <text x="635" y="488" font-family="serif" font-size="11" fill="#cbd5e1">(x + y)ⁿ = Σ (ⁿₖ) xⁿ⁻ᵏ yᵏ</text> <!-- Footer Branding --> <text x="450" y="545" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#475569" letter-spacing="2">WIKI MATHEMATICA • ANALYTIC GEOMETRY SERIES • MODULE 04</text> </svg>Analytic Geometry and Intro to Calculus image 1Analytic Geometry and Intro to Calculus - Precalculus 2e - image 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/analytic-geometry-and-intro-to-calculus/svg/1Analytic Geometry and Intro to Calculus diagram 1Analytic Geometry and Intro to Calculus - Precalculus 2e - diagram 1https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/analytic-geometry-and-intro-to-calculus/svg/2Analytic Geometry and Intro to Calculus diagram 2Analytic Geometry and Intro to Calculus - Precalculus 2e - diagram 2https://www.getlykke.com/explore/public/precalculus-2e-197c9158-ecc9-47fe-9183-c80854bf2e26/media/analytic-geometry-and-intro-to-calculus/svg/3Analytic Geometry and Intro to Calculus diagram 3Analytic Geometry and Intro to Calculus - Precalculus 2e - diagram 3https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c372026-04-20T04:56:53.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-weight="800" font-size="32" letter-spacing="2">COMPOSITE &amp; INVERSE FUNCTIONS</text> <path d="M 300 65 L 600 65" stroke="#38bdf8" stroke-width="2" stroke-linecap="round" opacity="0.6"/> <!-- LEFT PANEL: Composition --> <rect x="40" y="100" width="400" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="135" fill="#38bdf8" font-family="sans-serif" font-weight="700" font-size="18">FUNCTION COMPOSITION</text> <text x="60" y="155" fill="#94a3b8" font-family="sans-serif" font-size="12">The "Pipeline" of Mathematics: f(g(x))</text> <!-- Pipeline Graphic --> <g transform="translate(60, 180)"> <!-- Input --> <circle cx="20" cy="40" r="15" fill="#38bdf822" stroke="#38bdf8" stroke-width="2"/> <text x="20" y="44" text-anchor="middle" fill="#f8fafc" font-family="serif" font-style="italic" font-size="14">x</text> <!-- Arrow 1 --> <path d="M 35 40 L 75 40" stroke="#94a3b8" stroke-width="2" marker-end="url(#arrow)"/> <polygon points="75,40 68,36 68,44" fill="#94a3b8"/> <!-- Function g --> <rect x="80" y="20" width="50" height="40" rx="4" fill="#38bdf8" filter="url(#glow)"/> <text x="105" y="45" text-anchor="middle" fill="#0f172a" font-family="serif" font-weight="bold" font-size="18">g</text> <!-- Arrow 2 --> <path d="M 130 40 L 170 40" stroke="#94a3b8" stroke-width="2"/> <polygon points="170,40 163,36 163,44" fill="#94a3b8"/> <!-- Intermediate --> <text x="205" y="45" text-anchor="middle" fill="#f8fafc" font-family="serif" font-style="italic" font-size="14">g(x)</text> <!-- Arrow 3 --> <path d="M 240 40 L 280 40" stroke="#94a3b8" stroke-width="2"/> <polygon points="280,40 273,36 273,44" fill="#94a3b8"/> <!-- Function f --> <rect x="285" y="20" width="50" height="40" rx="4" fill="#e879f9" filter="url(#glow)"/> <text x="310" y="45" text-anchor="middle" fill="#0f172a" font-family="serif" font-weight="bold" font-size="18">f</text> <!-- Final Output --> <text x="310" y="85" text-anchor="middle" fill="#f8fafc" font-family="serif" font-style="italic" font-size="16" font-weight="bold">f(g(x))</text> </g> <!-- Note on Commutativity --> <rect x="60" y="285" width="360" height="40" rx="8" fill="#ef444415"/> <text x="240" y="310" text-anchor="middle" fill="#fca5a5" font-family="sans-serif" font-size="13" font-weight="600">Order Matters! f(g(x)) ≠ g(f(x))</text> <!-- RIGHT PANEL: Inverses --> <rect x="460" y="100" width="400" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="480" y="135" fill="#f59e0b" font-family="sans-serif" font-weight="700" font-size="18">INVERSE FUNCTIONS</text> <text x="480" y="155" fill="#94a3b8" font-family="sans-serif" font-size="12">The "Mirror" Property: Reflection across y = x</text> <!-- Graph Graphic --> <g transform="translate(640, 240)"> <!-- Axes --> <line x1="-80" y1="0" x2="80" y2="0" stroke="#94a3b8" stroke-width="1"/> <line x1="0" y1="-80" x2="0" y2="80" stroke="#94a3b8" stroke-width="1"/> <!-- y = x line --> <line x1="-70" y1="70" x2="70" y2="-70" stroke="#f8fafc" stroke-width="1" stroke-dasharray="4"/> <text x="55" y="-60" fill="#f8fafc" font-family="serif" font-size="10">y=x</text> <!-- f(x) = x^3 style curve --> <path d="M -60 60 Q -20 50 0 0 Q 20 -50 60 -60" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <text x="-75" y="45" fill="#38bdf8" font-family="serif" font-size="12" font-weight="bold">f(x)</text> <!-- f-1(x) reflection --> <path d="M 60 -60 Q 50 -20 0 0 Q -50 20 -60 60" fill="none" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <text x="65" y="-35" fill="#f59e0b" font-family="serif" font-size="12" font-weight="bold">f⁻¹(x)</text> </g> <text x="480" y="320" fill="#94a3b8" font-family="sans-serif" font-size="11">Swap x and y to find the inverse algebraically.</text> <!-- BOTTOM PANEL: Rules & Logic --> <rect x="40" y="360" width="820" height="160" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <!-- Horizontal Line Test --> <g transform="translate(70, 390)"> <text x="0" y="20" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="16">1. ONE-TO-ONE CHECK</text> <text x="0" y="40" fill="#94a3b8" font-family="sans-serif" font-size="12">Must pass the Horizontal Line Test (HLT).</text> <!-- Mini Graph Fail --> <g transform="translate(0, 55)"> <rect width="100" height="60" rx="4" fill="#00000033"/> <path d="M 10 50 Q 50 -20 90 50" fill="none" stroke="#38bdf8" stroke-width="2"/> <line x1="5" y1="25" x2="95" y2="25" stroke="#ef4444" stroke-width="1.5"/> <circle cx="28" cy="25" r="3" fill="#ef4444"/> <circle cx="72" cy="25" r="3" fill="#ef4444"/> <text x="50" y="55" text-anchor="middle" fill="#ef4444" font-family="sans-serif" font-size="9" font-weight="bold">FAIL (Not Invertible)</text> </g> <!-- Mini Graph Pass --> <g transform="translate(120, 55)"> <rect width="100" height="60" rx="4" fill="#00000033"/> <line x1="10" y1="50" x2="90" y2="10" stroke="#38bdf8" stroke-width="2"/> <line x1="5" y1="30" x2="95" y2="30" stroke="#22c55e" stroke-width="1.5"/> <circle cx="50" cy="30" r="3" fill="#22c55e"/> <text x="50" y="55" text-anchor="middle" fill="#22c55e" font-family="sans-serif" font-size="9" font-weight="bold">PASS (One-to-One)</text> </g> </g> <!-- Identity Property --> <g transform="translate(380, 390)"> <text x="0" y="20" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="16">2. THE IDENTITY LOOP</text> <text x="0" y="40" fill="#94a3b8" font-family="sans-serif" font-size="12">Inverses "undo" each other perfectly.</text> <rect x="0" y="55" width="220" height="60" rx="8" fill="#e879f911" stroke="#e879f944"/> <text x="110" y="90" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="20" font-weight="bold">f(f⁻¹(x)) = x</text> <path d="M 190 75 A 15 15 0 1 1 190 95" fill="none" stroke="#e879f9" stroke-width="2" marker-end="url(#arrow)"/> </g> <!-- Domain/Range Swap --> <g transform="translate(650, 390)"> <text x="0" y="20" fill="#f8fafc" font-family="sans-serif" font-weight="700" font-size="16">3. DOMAIN SWAP</text> <text x="0" y="45" fill="#38bdf8" font-family="sans-serif" font-size="12">Domain of f</text> <text x="100" y="45" fill="#f59e0b" font-family="sans-serif" font-size="12">Range of f⁻¹</text> <path d="M 75 42 L 95 42" stroke="#f8fafc" stroke-width="1"/> <text x="0" y="75" fill="#38bdf8" font-family="sans-serif" font-size="12">Range of f</text> <text x="100" y="75" fill="#f59e0b" font-family="sans-serif" font-size="12">Domain of f⁻¹</text> <path d="M 75 72 L 95 72" stroke="#f8fafc" stroke-width="1"/> <path d="M 0 55 L 160 55" stroke="#ffffff22" stroke-width="1"/> </g> <!-- Decorative elements --> <circle cx="40" cy="40" r="3" fill="#38bdf8"/> <circle cx="860" cy="40" r="3" fill="#f59e0b"/> <circle cx="40" cy="520" r="3" fill="#e879f9"/> <circle cx="860" cy="520" r="3" fill="#22c55e"/> </svg>Composite and Inverse Functions image 1Composite and Inverse Functions - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/composite-and-inverse-functions/svg/1Composite and Inverse Functions diagram 1Composite and Inverse Functions - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/composite-and-inverse-functions/svg/2Composite and Inverse Functions diagram 2Composite and Inverse Functions - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="30" height="30" patternUnits="userSpaceOnUse"> <circle cx="1" cy="1" r="1" fill="#334155" fill-opacity="0.5"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="40" y="50" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">TRIGONOMETRY &amp; SINUSOIDAL MODELS</text> <text x="40" y="75" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">FROM GEOMETRIC RATIOS TO PERIODIC PHENOMENA</text> <line x1="40" y1="90" x2="860" y2="90" stroke="#334155" stroke-width="1"/> <!-- Panel 1: The Unit Circle (Foundation) --> <rect x="40" y="110" width="260" height="410" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">01. THE UNIT CIRCLE</text> <text x="60" y="160" font-family="sans-serif" font-size="12" fill="#94a3b8">The bridge between geometry &amp; algebra.</text> <!-- Circle Graphic --> <circle cx="170" cy="260" r="70" fill="none" stroke="#334155" stroke-width="2" stroke-dasharray="4 2"/> <line x1="100" y1="260" x2="240" y2="260" stroke="#475569" stroke-width="1"/> <line x1="170" y1="190" x2="170" y2="330" stroke="#475569" stroke-width="1"/> <!-- Triangle inside circle --> <path d="M 170,260 L 220,210 L 220,260 Z" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <circle cx="220" cy="210" r="4" fill="#e879f9" filter="url(#glow)"/> <text x="228" y="205" font-family="serif" font-style="italic" font-size="12" fill="#f8fafc">P(x, y)</text> <text x="185" y="252" font-family="serif" font-size="14" fill="#f59e0b">θ</text> <!-- Identities --> <rect x="60" y="360" width="220" height="140" rx="8" fill="#00000030"/> <text x="75" y="385" font-family="serif" font-size="14" fill="#f8fafc">x = cos(θ)</text> <text x="75" y="405" font-family="serif" font-size="14" fill="#f8fafc">y = sin(θ)</text> <text x="75" y="435" font-family="sans-serif" font-weight="700" font-size="13" fill="#e879f9">Pythagorean Identity:</text> <text x="75" y="455" font-family="serif" font-size="16" fill="#f8fafc">sin²θ + cos²θ = 1</text> <text x="75" y="485" font-family="sans-serif" font-size="11" fill="#94a3b8">Valid for all real numbers θ.</text> <!-- Panel 2: Sinusoidal Evolution --> <rect x="320" y="110" width="260" height="410" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="340" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">02. PERIODICITY</text> <text x="340" y="160" font-family="sans-serif" font-size="12" fill="#94a3b8">Rotation over time yields a wave.</text> <!-- Waveform Graphic --> <path d="M 340,280 L 560,280" stroke="#475569" stroke-width="1"/> <path d="M 340,220 L 340,340" stroke="#475569" stroke-width="1"/> <path d="M 340,280 Q 367.5,180 395,280 T 450,280 T 505,280 T 560,280" fill="none" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <text x="350" y="210" font-family="sans-serif" font-size="11" fill="#f59e0b" font-weight="bold">AMPLITUDE</text> <line x1="395" y1="280" x2="505" y2="280" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2"/> <text x="415" y="300" font-family="sans-serif" font-size="11" fill="#38bdf8" font-weight="bold">PERIOD (2π)</text> <text x="340" y="380" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">The Standard Model:</text> <text x="340" y="405" font-family="serif" font-size="18" fill="#f59e0b">y = A sin(B(x - C)) + D</text> <g font-family="sans-serif" font-size="11" fill="#94a3b8"> <text x="340" y="435">• A: Amplitude (Stretch)</text> <text x="340" y="455">• B: Frequency (Period = 2π/B)</text> <text x="340" y="475">• C: Phase Shift (Horizontal)</text> <text x="340" y="495">• D: Vertical Shift (Midline)</text> </g> <!-- Panel 3: Inverse & General (Top) --> <rect x="600" y="110" width="260" height="195" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">03. INVERSE FUNCTIONS</text> <text x="620" y="160" font-family="sans-serif" font-size="12" fill="#94a3b8">Restricting domain for uniqueness.</text> <rect x="620" y="180" width="220" height="100" rx="8" fill="#00000030"/> <g font-family="sans-serif" font-size="11" fill="#f8fafc"> <text x="635" y="205" font-weight="bold" fill="#e879f9">Function</text> <text x="730" y="205" font-weight="bold" fill="#e879f9">Principal Range</text> <text x="635" y="230">sin⁻¹(x)</text> <text x="730" y="230">[-π/2, π/2]</text> <text x="635" y="250">cos⁻¹(x)</text> <text x="730" y="250">[0, π]</text> <text x="635" y="270">tan⁻¹(x)</text> <text x="730" y="270">(-π/2, π/2)</text> </g> <!-- Panel 4: General Triangles (Bottom) --> <rect x="600" y="325" width="260" height="195" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="355" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">04. OBLIQUE LAWS</text> <path d="M 630,430 L 710,430 L 670,390 Z" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="665" y="385" font-family="serif" font-size="10" fill="#94a3b8">C</text> <text x="620" y="435" font-family="serif" font-size="10" fill="#94a3b8">A</text> <text x="715" y="435" font-family="serif" font-size="10" fill="#94a3b8">B</text> <text x="620" y="460" font-family="sans-serif" font-weight="700" font-size="12" fill="#f8fafc">Law of Sines:</text> <text x="620" y="478" font-family="serif" font-size="14" fill="#38bdf8">a/sinA = b/sinB = c/sinC</text> <text x="620" y="500" font-family="sans-serif" font-weight="700" font-size="12" fill="#f8fafc">Law of Cosines:</text> <text x="620" y="515" font-family="serif" font-size="13" fill="#38bdf8">c² = a² + b² - 2ab cosC</text> <!-- Decorative elements --> <circle cx="850" cy="50" r="20" fill="none" stroke="#f59e0b" stroke-width="1" stroke-dasharray="2 2"/> <path d="M 840,50 L 860,50 M 850,40 L 850,60" stroke="#f59e0b" stroke-width="1"/> </svg>Trigonometry and Sinusoidal Models image 1Trigonometry and Sinusoidal Models - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/trigonometry-and-sinusoidal-models/svg/1Trigonometry and Sinusoidal Models diagram 1Trigonometry and Sinusoidal Models - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/trigonometry-and-sinusoidal-models/svg/2Trigonometry and Sinusoidal Models diagram 2Trigonometry and Sinusoidal Models - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff08" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="blur" /> <feComposite in="SourceGraphic" in2="blur" operator="over" /> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="bold" font-size="32" fill="#f8fafc">COMPLEX NUMBERS &amp; POLAR FORM</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">TRANSITIONING FROM ALGEBRAIC GRID TO GEOMETRIC ROTATION</text> <!-- Left Panel: Rectangular Form --> <rect x="40" y="110" width="260" height="240" rx="16" fill="#ffffff10" stroke="#ffffff20" stroke-width="1"/> <text x="60" y="140" font-family="sans-serif" font-weight="bold" font-size="18" fill="#e879f9">Rectangular Form</text> <text x="60" y="165" font-family="serif" font-style="italic" font-size="22" fill="#f8fafc">z = a + bi</text> <g transform="translate(70, 190)"> <line x1="0" y1="100" x2="100" y2="100" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4"/> <line x1="0" y1="100" x2="0" y2="0" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4"/> <rect x="0" y="30" width="70" height="70" fill="#e879f920" stroke="#e879f9" stroke-width="2"/> <text x="35" y="115" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#94a3b8">Real (a)</text> <text x="-10" y="65" text-anchor="end" font-family="sans-serif" font-size="12" fill="#94a3b8" transform="rotate(-90, -10, 65)">Imaginary (b)</text> <circle cx="70" cy="30" r="4" fill="#f8fafc"/> </g> <text x="60" y="325" font-family="sans-serif" font-size="12" fill="#94a3b8" width="220"> <tspan x="60" dy="0">Best for addition and subtraction.</tspan> <tspan x="60" dy="16">Visualized as a point on a grid.</tspan> </text> <!-- Center: The Bridge (Main Diagram) --> <g transform="translate(450, 240)"> <!-- Axes --> <line x1="-120" y1="0" x2="120" y2="0" stroke="#475569" stroke-width="1"/> <line x1="0" y1="-120" x2="0" y2="120" stroke="#475569" stroke-width="1"/> <text x="125" y="5" font-family="sans-serif" font-size="12" fill="#475569">Re</text> <text x="5" y="-125" font-family="sans-serif" font-size="12" fill="#475569">Im</text> <!-- Unit Circle Reference --> <circle cx="0" cy="0" r="100" fill="none" stroke="#ffffff08" stroke-width="1"/> <!-- Vector z --> <line x1="0" y1="0" x2="86.6" y2="-50" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <circle cx="86.6" cy="-50" r="5" fill="#f59e0b"/> <!-- Angle Arc --> <path d="M 30 0 A 30 30 0 0 0 25.98 -15" fill="none" stroke="#38bdf8" stroke-width="2"/> <!-- Labels --> <text x="45" y="-35" font-family="serif" font-style="italic" font-size="18" fill="#f59e0b">r</text> <text x="35" y="-8" font-family="serif" font-style="italic" font-size="18" fill="#38bdf8">θ</text> <text x="95" y="-60" font-family="serif" font-weight="bold" font-size="20" fill="#f8fafc">z</text> </g> <!-- Right Panel: Polar Form --> <rect x="600" y="110" width="260" height="240" rx="16" fill="#ffffff10" stroke="#ffffff20" stroke-width="1"/> <text x="620" y="140" font-family="sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">Polar Form</text> <text x="620" y="165" font-family="serif" font-style="italic" font-size="22" fill="#f8fafc">z = r(cos θ + i sin θ)</text> <g transform="translate(630, 190)"> <circle cx="50" cy="50" r="45" fill="none" stroke="#38bdf840" stroke-width="1" stroke-dasharray="4"/> <line x1="50" y1="50" x2="85" y2="20" stroke="#f59e0b" stroke-width="2"/> <path d="M 70 50 A 20 20 0 0 0 65 35" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="90" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">Magnitude &amp; Phase</text> </g> <text x="620" y="325" font-family="sans-serif" font-size="12" fill="#94a3b8"> <tspan x="620" dy="0">Best for multiplication and powers.</tspan> <tspan x="620" dy="16">Visualized as rotation and scaling.</tspan> </text> <!-- Bottom Section: Euler's Formula & Operations --> <rect x="40" y="370" width="820" height="160" rx="16" fill="#ffffff05" stroke="#ffffff10" stroke-width="1"/> <!-- Euler's Formula --> <g transform="translate(60, 400)"> <text x="0" y="20" font-family="sans-serif" font-weight="bold" font-size="16" fill="#f59e0b">EULER'S FORMULA</text> <rect x="0" y="35" width="240" height="60" rx="8" fill="#f59e0b10" stroke="#f59e0b40"/> <text x="120" y="75" text-anchor="middle" font-family="serif" font-size="24" fill="#f8fafc">e<tspan baseline-shift="super" font-size="16">iθ</tspan> = cos θ + i sin θ</text> <text x="0" y="115" font-family="sans-serif" font-size="12" fill="#94a3b8">The exponential bridge to rotation.</text> </g> <!-- Arithmetic Rules --> <g transform="translate(360, 400)"> <text x="0" y="20" font-family="sans-serif" font-weight="bold" font-size="16" fill="#38bdf8">MULTIPLICATION RULE</text> <text x="0" y="55" font-family="serif" font-size="18" fill="#f8fafc">z<tspan baseline-shift="sub" font-size="12">1</tspan>z<tspan baseline-shift="sub" font-size="12">2</tspan> = r<tspan baseline-shift="sub" font-size="12">1</tspan>r<tspan baseline-shift="sub" font-size="12">2</tspan> e<tspan baseline-shift="super" font-size="12">i(θ₁+θ₂)</tspan></text> <path d="M 0 75 L 200 75" stroke="#ffffff20" stroke-width="1"/> <text x="0" y="100" font-family="sans-serif" font-size="13" fill="#f8fafc">Multiply Moduli | <tspan fill="#38bdf8">Add Arguments</tspan></text> <text x="0" y="118" font-family="sans-serif" font-size="12" fill="#94a3b8">Multiplication becomes a geometric spin.</text> </g> <!-- Conversion Formulas --> <g transform="translate(650, 400)"> <text x="0" y="20" font-family="sans-serif" font-weight="bold" font-size="16" fill="#94a3b8">CONVERSION</text> <text x="0" y="50" font-family="serif" font-size="14" fill="#f8fafc">r = √(a² + b²)</text> <text x="0" y="75" font-family="serif" font-size="14" fill="#f8fafc">θ = atan2(b, a)</text> <text x="0" y="100" font-family="serif" font-size="14" fill="#f8fafc">a = r cos θ</text> <text x="0" y="125" font-family="serif" font-size="14" fill="#f8fafc">b = r sin θ</text> </g> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#e879f920" stroke-width="2"/> <circle cx="850" cy="50" r="15" fill="none" stroke="#e879f940" stroke-width="1"/> <path d="M 40 50 L 150 50" stroke="#f59e0b" stroke-width="2" stroke-linecap="round"/> </svg>Complex Numbers and Polar Form image 1Complex Numbers and Polar Form - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/complex-numbers-and-polar-form/svg/1Complex Numbers and Polar Form diagram 1Complex Numbers and Polar Form - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/complex-numbers-and-polar-form/svg/2Complex Numbers and Polar Form diagram 2Complex Numbers and Polar Form - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <filter id="cardShadow"> <feDropShadow dx="0" dy="4" stdDeviation="8" flood-opacity="0.3"/> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Decorative Geometry --> <circle cx="850" cy="50" r="100" fill="#38bdf808" /> <path d="M-50 400 L150 600 L-50 600 Z" fill="#e879f905" /> <!-- Header --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="-0.5">RATIONAL FUNCTIONS</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="400" fill="#94a3b8" text-transform="uppercase" letter-spacing="2">The Architecture of Singularities &amp; Asymptotes</text> <!-- Left Card: Definition & Arithmetic --> <rect x="40" y="120" width="250" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15" filter="url(#cardShadow)"/> <text x="60" y="155" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">The Foundation</text> <text x="60" y="185" font-family="serif" font-size="20" font-style="italic" fill="#f8fafc">R(x) = P(x) / Q(x)</text> <text x="60" y="210" font-family="sans-serif" font-size="12" fill="#94a3b8" width="210"> <tspan x="60" dy="0">A ratio of two polynomials where</tspan> <tspan x="60" dy="16">the denominator Q(x) ≠ 0.</tspan> </text> <line x1="60" y1="245" x2="270" y2="245" stroke="#ffffff15" /> <text x="60" y="275" font-family="sans-serif" font-size="16" font-weight="700" fill="#f8fafc">Arithmetic Bridge</text> <!-- Arithmetic Icons/Steps --> <g transform="translate(60, 295)"> <rect width="24" height="24" rx="6" fill="#38bdf820" /> <text x="12" y="17" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#38bdf8">×</text> <text x="35" y="16" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Multiply</text> <text x="35" y="30" font-family="sans-serif" font-size="11" fill="#94a3b8">Factor first, then cancel.</text> </g> <g transform="translate(60, 345)"> <rect width="24" height="24" rx="6" fill="#e879f920" /> <text x="12" y="17" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#e879f9">÷</text> <text x="35" y="16" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Divide</text> <text x="35" y="30" font-family="sans-serif" font-size="11" fill="#94a3b8">Multiply by the reciprocal.</text> </g> <g transform="translate(60, 395)"> <rect width="24" height="24" rx="6" fill="#f59e0b20" /> <text x="12" y="17" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f59e0b">+</text> <text x="35" y="16" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Add/Sub</text> <text x="35" y="30" font-family="sans-serif" font-size="11" fill="#94a3b8">Find the LCM denominator.</text> </g> <!-- Center Card: Visual Graph --> <rect x="310" y="120" width="280" height="400" rx="16" fill="#ffffff12" stroke="#38bdf830" filter="url(#cardShadow)"/> <!-- Coordinate System --> <g transform="translate(450, 340)"> <!-- Grid --> <line x1="-120" y1="0" x2="120" y2="0" stroke="#94a3b840" stroke-width="1" /> <line x1="0" y1="-150" x2="0" y2="80" stroke="#94a3b840" stroke-width="1" /> <!-- Vertical Asymptote --> <line x1="-40" y1="-150" x2="-40" y2="80" stroke="#e879f9" stroke-width="2" stroke-dasharray="6,4" /> <text x="-45" y="95" text-anchor="end" font-family="sans-serif" font-size="10" fill="#e879f9" font-weight="bold">V.A. x = c</text> <!-- Curve Part 1 --> <path d="M -120 -10 Q -60 -15 -45 -150" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <!-- Curve Part 2 with Hole --> <path d="M -35 80 Q -20 10 40 10 L 120 10" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <!-- Hole --> <circle cx="60" cy="10" r="5" fill="#1e1b4b" stroke="#f59e0b" stroke-width="2" /> <text x="65" y="-5" font-family="sans-serif" font-size="10" fill="#f59e0b" font-weight="bold">HOLE (Removable)</text> <text x="0" y="-170" text-anchor="middle" font-family="sans-serif" font-size="16" font-weight="700" fill="#f8fafc">Visual Anatomy</text> </g> <!-- Right Card: Discontinuities --> <rect x="610" y="120" width="250" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15" filter="url(#cardShadow)"/> <text x="630" y="155" font-family="sans-serif" font-size="18" font-weight="700" fill="#e879f9">The Breaks</text> <!-- Hole Section --> <g transform="translate(630, 180)"> <text x="0" y="0" font-family="sans-serif" font-size="14" font-weight="700" fill="#f59e0b">Removable (Holes)</text> <rect y="10" width="210" height="75" rx="8" fill="#f59e0b10" /> <text x="10" y="30" font-family="sans-serif" font-size="11" fill="#f8fafc"> <tspan x="10" dy="0">Occurs when a factor (x - c)</tspan> <tspan x="10" dy="15">exists in both P(x) and Q(x).</tspan> <tspan x="10" dy="20" fill="#94a3b8" font-style="italic">The limit exists, but the</tspan> <tspan x="10" dy="15" fill="#94a3b8" font-style="italic">point is missing.</tspan> </text> </g> <!-- Asymptote Section --> <g transform="translate(630, 285)"> <text x="0" y="0" font-family="sans-serif" font-size="14" font-weight="700" fill="#e879f9">Non-Removable (V.A.)</text> <rect y="10" width="210" height="75" rx="8" fill="#e879f910" /> <text x="10" y="30" font-family="sans-serif" font-size="11" fill="#f8fafc"> <tspan x="10" dy="0">Occurs when (x - c) remains</tspan> <tspan x="10" dy="15">in the denominator after</tspan> <tspan x="10" dy="20" fill="#94a3b8" font-style="italic">simplification. The function</tspan> <tspan x="10" dy="15" fill="#94a3b8" font-style="italic">shoots to ± Infinity.</tspan> </text> </g> <!-- End Behavior --> <g transform="translate(630, 390)"> <text x="0" y="0" font-family="sans-serif" font-size="14" font-weight="700" fill="#38bdf8">End Behavior</text> <text x="0" y="25" font-family="sans-serif" font-size="11" fill="#f8fafc">Determined by degrees (n, m):</text> <g transform="translate(0, 40)"> <text x="0" y="0" font-family="sans-serif" font-size="10" fill="#94a3b8">n &lt; m : y = 0 (H.A.)</text> <text x="0" y="15" font-family="sans-serif" font-size="10" fill="#94a3b8">n = m : y = leading coeff ratio</text> <text x="0" y="30" font-family="sans-serif" font-size="10" fill="#94a3b8">n &gt; m : Slant Asymptote</text> </g> </g> <!-- Footer / Domain Note --> <rect x="310" y="475" width="280" height="45" rx="12" fill="#38bdf815" stroke="#38bdf840" /> <text x="450" y="493" text-anchor="middle" font-family="sans-serif" font-size="11" font-weight="bold" fill="#38bdf8">DOMAIN PRESERVATION</text> <text x="450" y="508" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f8fafc">Always track original restrictions, even after canceling factors!</text> </svg>Rational Functions image 1Rational Functions - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/rational-functions/svg/1Rational Functions diagram 1Rational Functions - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/rational-functions/svg/2Rational Functions diagram 2Rational Functions - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="cardGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#ffffff15"/> <stop offset="100%" stop-color="#ffffff05"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background and Grid --> <rect width="900" height="560" fill="url(#bg)"/> <g stroke="#ffffff08" stroke-width="1"> <path d="M0 40h900M0 80h900M0 120h900M0 160h900M0 200h900M0 240h900M0 280h900M0 320h900M0 360h900M0 400h900M0 440h900M0 480h900M0 520h900"/> <path d="M40 0v560M80 0v560M120 0v560M160 0v560M200 0v560M240 0v560M280 0v560M320 0v560M360 0v560M400 0v560M440 0v560M480 0v560M520 0v560M560 0v560M600 0v560M640 0v560M680 0v560M720 0v560M760 0v560M800 0v560M840 0v560M880 0v560"/> </g> <!-- Header Section --> <text x="40" y="60" font-family="Arial, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-1">CONIC SECTIONS</text> <text x="40" y="85" font-family="Arial, sans-serif" font-size="14" fill="#94a3b8" font-weight="400">The Geometric Language of the Physical Universe</text> <rect x="40" y="100" width="180" height="4" fill="#38bdf8" rx="2"/> <!-- Central Illustration: The Double Cone --> <g transform="translate(450, 280)"> <!-- Cones --> <path d="M-80,-150 L80,-150 L0,0 Z" fill="#ffffff10" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4 2"/> <path d="M-80,150 L80,150 L0,0 Z" fill="#ffffff10" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4 2"/> <!-- Slicing Planes (Stylized) --> <path d="M-100,-110 L100,-110 L120,-90 L-80,-90 Z" fill="#38bdf830" stroke="#38bdf8" stroke-width="1.5"/> <!-- Circle Plane --> <path d="M-100,20 L100,70 L120,90 L-80,40 Z" fill="#e879f930" stroke="#e879f9" stroke-width="1.5"/> <!-- Ellipse Plane --> <!-- Labels for Cone --> <text x="90" y="-100" font-family="Arial, sans-serif" font-size="11" fill="#38bdf8" font-weight="bold">CIRCLE (θ = 90°)</text> <text x="110" y="60" font-family="Arial, sans-serif" font-size="11" fill="#e879f9" font-weight="bold">ELLIPSE (θ &gt; α)</text> <text x="-160" y="120" font-family="Arial, sans-serif" font-size="11" fill="#f59e0b" font-weight="bold">PARABOLA (θ = α)</text> <text x="-160" y="-40" font-family="Arial, sans-serif" font-size="11" fill="#f43f5e" font-weight="bold">HYPERBOLA (θ &lt; α)</text> </g> <!-- Info Cards --> <!-- Circle Card --> <rect x="40" y="140" width="180" height="110" rx="16" fill="url(#cardGrad)" stroke="#ffffff10"/> <circle cx="70" cy="175" r="20" fill="none" stroke="#38bdf8" stroke-width="2" filter="url(#glow)"/> <text x="100" y="175" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">Circle</text> <text x="60" y="210" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Eccentricity: e = 0</text> <text x="60" y="228" font-family="Arial, sans-serif" font-size="11" fill="#38bdf8">x² + y² = r²</text> <!-- Ellipse Card --> <rect x="40" y="265" width="180" height="110" rx="16" fill="url(#cardGrad)" stroke="#ffffff10"/> <ellipse cx="70" cy="300" rx="25" ry="15" fill="none" stroke="#e879f9" stroke-width="2" filter="url(#glow)"/> <text x="105" y="300" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">Ellipse</text> <text x="60" y="335" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">0 &lt; e &lt; 1</text> <text x="60" y="353" font-family="Arial, sans-serif" font-size="11" fill="#e879f9">d₁ + d₂ = 2a</text> <!-- Parabola Card --> <rect x="680" y="140" width="180" height="110" rx="16" fill="url(#cardGrad)" stroke="#ffffff10"/> <path d="M695,185 Q710,155 725,185" fill="none" stroke="#f59e0b" stroke-width="2" filter="url(#glow)"/> <text x="735" y="175" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">Parabola</text> <text x="700" y="210" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Eccentricity: e = 1</text> <text x="700" y="228" font-family="Arial, sans-serif" font-size="11" fill="#f59e0b">y² = 4ax</text> <!-- Hyperbola Card --> <rect x="680" y="265" width="180" height="110" rx="16" fill="url(#cardGrad)" stroke="#ffffff10"/> <path d="M695,285 Q710,300 695,315 M725,285 Q710,300 725,315" fill="none" stroke="#f43f5e" stroke-width="2" filter="url(#glow)"/> <text x="735" y="300" font-family="Arial, sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">Hyperbola</text> <text x="700" y="335" font-family="Arial, sans-serif" font-size="12" fill="#94a3b8">Eccentricity: e &gt; 1</text> <text x="700" y="353" font-family="Arial, sans-serif" font-size="11" fill="#f43f5e">|d₁ - d₂| = 2a</text> <!-- Bottom Panel: General Equation --> <rect x="40" y="420" width="820" height="100" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="70" y="455" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#38bdf8" text-transform="uppercase">The General Second-Degree Equation</text> <text x="70" y="485" font-family="serif" font-size="24" fill="#f8fafc" font-style="italic">Ax² + Bxy + Cy² + Dx + Ey + F = 0</text> <!-- Discriminant Key --> <line x1="450" y1="435" x2="450" y2="505" stroke="#ffffff20" stroke-width="1"/> <text x="475" y="455" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#94a3b8">DISCRIMINANT: Δ = B² - 4AC</text> <g font-family="Arial, sans-serif" font-size="11"> <text x="475" y="475" fill="#f8fafc">Δ &lt; 0 : Ellipse / Circle</text> <text x="475" y="495" fill="#f8fafc">Δ = 0 : Parabola</text> <text x="620" y="475" fill="#f8fafc">Δ &gt; 0 : Hyperbola</text> <text x="620" y="495" fill="#f8fafc">B = 0, A = C : Circle</text> </g> <!-- Decorative Elements --> <circle cx="840" cy="60" r="15" fill="none" stroke="#ffffff20" stroke-width="1"/> <circle cx="840" cy="60" r="8" fill="#f59e0b" opacity="0.6"/> <path d="M820,40 L860,80" stroke="#ffffff10" stroke-width="1"/> </svg>Conic Sections image 1Conic Sections - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/conic-sections/svg/1Conic Sections diagram 1Conic Sections - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/conic-sections/svg/2Conic Sections diagram 2Conic Sections - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <!-- Background Gradient --> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <!-- Card Gradient --> <linearGradient id="cardGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#ffffff15"/> <stop offset="100%" stop-color="#ffffff05"/> </linearGradient> <!-- Arrow Markers --> <marker id="arrowhead-blue" markerWidth="10" markerHeight="7" refX="9" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="#38bdf8" /> </marker> <marker 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stroke-width="2" stroke-linecap="round"/> <!-- Left Column: Comparison --> <rect x="40" y="120" width="260" height="400" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="60" y="155" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">Scalar vs. Vector</text> <!-- Scalar Section --> <circle cx="75" cy="200" r="15" fill="#94a3b833" stroke="#94a3b8" stroke-width="1"/> <text x="105" y="195" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Scalar</text> <text x="105" y="212" font-family="sans-serif" font-size="12" fill="#94a3b8">Magnitude only (e.g., Mass, Temp)</text> <!-- Vector Section --> <line x1="60" y1="260" x2="90" y2="240" stroke="#f59e0b" stroke-width="3" marker-end="url(#arrowhead-gold)"/> <text x="105" y="250" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Vector</text> <text x="105" y="267" font-family="sans-serif" font-size="12" fill="#94a3b8">Magnitude + Direction (Force, Velocity)</text> <rect x="55" y="300" width="230" height="1" fill="#ffffff10"/> <!-- Comparison Table --> <text x="60" y="330" font-family="sans-serif" font-size="11" font-weight="700" fill="#38bdf8">PROPERTY</text> <text x="150" y="330" font-family="sans-serif" font-size="11" font-weight="700" fill="#38bdf8">SCALAR</text> <text x="230" y="330" font-family="sans-serif" font-size="11" font-weight="700" fill="#38bdf8">VECTOR</text> <text x="60" y="355" font-family="sans-serif" font-size="11" fill="#f8fafc">Notation</text> <text x="150" y="355" font-family="sans-serif" font-size="11" fill="#94a3b8" font-style="italic">s</text> <text x="230" y="355" font-family="sans-serif" font-size="11" fill="#94a3b8" font-weight="bold">v</text> <text x="60" y="380" font-family="sans-serif" font-size="11" fill="#f8fafc">Tensor Rank</text> <text x="150" y="380" font-family="sans-serif" font-size="11" fill="#94a3b8">0</text> <text x="230" y="380" font-family="sans-serif" font-size="11" fill="#94a3b8">1</text> <!-- Middle Column: Geometric Ops --> <rect x="320" y="120" width="260" height="400" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="340" y="155" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">Vector Addition</text> <!-- Tip-to-Tail Diagram --> <g transform="translate(360, 280)"> <!-- Grid lines --> <line x1="0" y1="0" x2="180" y2="0" stroke="#ffffff10" stroke-width="1"/> <line x1="0" y1="0" x2="0" y2="-120" stroke="#ffffff10" stroke-width="1"/> <!-- Vector U --> <line x1="0" y1="0" x2="80" y2="-30" stroke="#38bdf8" stroke-width="3" marker-end="url(#arrowhead-blue)"/> <text x="35" y="-25" font-family="sans-serif" font-size="12" fill="#38bdf8" font-weight="bold">u</text> <!-- Vector V --> <line x1="80" y1="-30" x2="140" y2="-100" stroke="#e879f9" stroke-width="3" marker-end="url(#arrowhead-pink)"/> <text x="115" y="-75" font-family="sans-serif" font-size="12" fill="#e879f9" font-weight="bold">v</text> <!-- Resultant --> <line x1="0" y1="0" x2="135" y2="-95" stroke="#f59e0b" stroke-width="3" stroke-dasharray="4" marker-end="url(#arrowhead-gold)"/> <text x="50" y="-65" font-family="sans-serif" font-size="13" fill="#f59e0b" font-weight="bold">u + v</text> </g> <text x="340" y="440" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="600">Tip-to-Tail Method</text> <text x="340" y="460" font-family="sans-serif" font-size="12" fill="#94a3b8" width="220"> Place the tail of v at the tip of u. </text> <text x="340" y="476" font-family="sans-serif" font-size="12" fill="#94a3b8"> The resultant connects the start to end. </text> <!-- Right Column: Algebra --> <rect x="600" y="120" width="260" height="400" rx="16" fill="url(#cardGrad)" stroke="#ffffff10" stroke-width="1"/> <text x="620" y="155" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">Components</text> <!-- Component Diagram --> <g transform="translate(640, 300)"> <path d="M 0 0 L 120 0 L 120 -80 Z" fill="#38bdf810" stroke="#38bdf8" stroke-width="1" stroke-dasharray="2"/> <line x1="0" y1="0" x2="115" y2="-77" stroke="#f8fafc" stroke-width="3" marker-end="url(#arrowhead-gold)"/> <text x="50" y="15" font-family="serif" font-size="14" fill="#38bdf8" font-style="italic">vₓ</text> <text x="130" y="-35" font-family="serif" font-size="14" fill="#38bdf8" font-style="italic">vᵧ</text> <text x="40" y="-50" font-family="serif" font-size="14" fill="#f8fafc" font-weight="bold">||v||</text> </g> <!-- Formulas --> <rect x="620" y="340" width="220" height="140" rx="8" fill="#00000020"/> <text x="635" y="365" font-family="serif" font-size="14" fill="#f8fafc">Magnitude:</text> <text x="635" y="385" font-family="serif" font-size="16" fill="#f59e0b">||v|| = √(vₓ² + vᵧ²)</text> <text x="635" y="420" font-family="serif" font-size="14" fill="#f8fafc">Unit Vector:</text> <text x="635" y="440" font-family="serif" font-size="16" fill="#38bdf8">û = v / ||v||</text> <text x="635" y="470" font-family="serif" font-size="12" fill="#94a3b8">Scaling: k·v = ⟨kx, ky⟩</text> <!-- Decorative Footer --> <circle cx="450" cy="540" r="3" fill="#38bdf8"/> <circle cx="470" cy="540" r="3" fill="#e879f9"/> <circle cx="430" cy="540" r="3" fill="#f59e0b"/> </svg>Vectors image 1Vectors - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/vectors/svg/1Vectors diagram 1Vectors - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/vectors/svg/2Vectors diagram 2Vectors - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg-grad" x1="0%" y1="0%" x2="0%" y2="100%"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="30" height="30" patternUnits="userSpaceOnUse"> <path d="M 30 0 L 0 0 0 30" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg-grad)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="40" y="50" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">MATRICES</text> <text x="40" y="75" font-family="sans-serif" font-weight="400" font-size="14" fill="#38bdf8" letter-spacing="3">THE ENGINES OF LINEAR ALGEBRA</text> <line x1="40" y1="90" x2="320" y2="90" stroke="#38bdf8" stroke-width="2" opacity="0.5"/> <!-- Left Panel: The Mechanics --> <rect x="40" y="115" width="260" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="145" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">01. THE MECHANICS</text> <text x="60" y="165" font-family="sans-serif" font-size="12" fill="#94a3b8">Composition via Dot Product</text> <!-- Matrix Multiplication Visual --> <g transform="translate(65, 190)"> <!-- Matrix A --> <rect x="0" y="0" width="40" height="60" rx="4" fill="#ffffff10" stroke="#94a3b8"/> <rect x="2" y="10" width="36" height="12" fill="#38bdf830" stroke="#38bdf8" stroke-width="1"/> <text x="20" y="-10" text-anchor="middle" font-family="monospace" font-size="10" fill="#94a3b8">Row i</text> <text x="50" y="35" font-family="sans-serif" font-size="16" fill="#f8fafc">×</text> <!-- Matrix B --> <rect x="70" y="0" width="60" height="60" rx="4" fill="#ffffff10" stroke="#94a3b8"/> <rect x="100" y="2" width="12" height="56" fill="#e879f930" stroke="#e879f9" stroke-width="1"/> <text x="106" y="-10" text-anchor="middle" font-family="monospace" font-size="10" fill="#94a3b8">Col j</text> <text x="145" y="35" font-family="sans-serif" font-size="16" fill="#f8fafc">=</text> <!-- Result C --> <rect x="170" y="0" width="40" height="60" rx="4" fill="#ffffff10" stroke="#94a3b8"/> <circle cx="190" cy="16" r="4" fill="#f59e0b" filter="url(#glow)"/> <text x="190" y="-10" text-anchor="middle" font-family="monospace" font-size="10" fill="#94a3b8">c[i,j]</text> </g> <text x="60" y="300" font-family="monospace" font-size="11" fill="#f8fafc">c_ij = Σ (a_ik * b_kj)</text> <text x="60" y="325" font-family="sans-serif" font-size="11" fill="#94a3b8" font-style="italic">Order matters: AB ≠ BA</text> <!-- Center Panel: The Geometry --> <rect x="320" y="115" width="540" height="320" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="340" y="145" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">02. GEOMETRIC MAPPING</text> <text x="340" y="165" font-family="sans-serif" font-size="12" fill="#94a3b8">Matrices as Linear Transformations</text> <!-- Coordinate System --> <g transform="translate(450, 310)"> <!-- Grid lines --> <path d="M -100 0 L 100 0 M 0 -100 L 0 100" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4"/> <!-- Transformed Shape (Shear) --> <path d="M 0 0 L 60 0 L 90 -60 L 30 -60 Z" fill="#38bdf820" stroke="#38bdf8" stroke-width="2" filter="url(#glow)"/> <!-- Original Unit Square --> <rect x="0" y="-60" width="60" height="60" fill="none" stroke="#ffffff30" stroke-width="1" stroke-dasharray="2"/> <!-- Basis Vectors --> <line x1="0" y1="0" x2="60" y2="0" stroke="#fb7185" stroke-width="3" marker-end="url(#arrow-red)"/> <line x1="0" y1="0" x2="30" y2="-60" stroke="#fbbf24" stroke-width="3" marker-end="url(#arrow-gold)"/> <text x="65" y="15" font-family="monospace" font-size="12" font-weight="bold" fill="#fb7185">i-hat [1,0]</text> <text x="10" y="-75" font-family="monospace" font-size="12" font-weight="bold" fill="#fbbf24">j-hat [k,1]</text> </g> <!-- Transformation Matrix Label --> <g transform="translate(680, 200)"> <text x="0" y="0" font-family="serif" font-size="24" fill="#f8fafc">[</text> <text x="45" y="0" font-family="serif" font-size="24" fill="#f8fafc">]</text> <text x="12" y="-12" font-family="monospace" font-size="14" fill="#fb7185">1</text> <text x="12" y="8" font-family="monospace" font-size="14" fill="#fb7185">0</text> <text x="32" y="-12" font-family="monospace" font-size="14" fill="#fbbf24">k</text> <text x="32" y="8" font-family="monospace" font-size="14" fill="#fbbf24">1</text> <text x="-70" y="0" font-family="sans-serif" font-size="12" fill="#94a3b8">Shear Matrix:</text> </g> <!-- Bottom Panel: Applications --> <rect x="40" y="375" width="260" height="150" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="405" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">03. APPLICATIONS</text> <g transform="translate(60, 425)"> <circle cx="15" cy="15" r="12" fill="#38bdf820" stroke="#38bdf8"/> <path d="M 10 20 L 15 10 L 20 20 Z" fill="#38bdf8"/> <text x="40" y="18" font-family="sans-serif" font-size="12" fill="#f8fafc">Computer Graphics</text> <circle cx="15" cy="45" r="12" fill="#e879f920" stroke="#e879f9"/> <circle cx="12" cy="42" r="2" fill="#e879f9"/> <circle cx="18" cy="42" r="2" fill="#e879f9"/> <circle cx="15" cy="48" r="2" fill="#e879f9"/> <text x="40" y="48" font-family="sans-serif" font-size="12" fill="#f8fafc">Neural Networks</text> <circle cx="15" cy="75" r="12" fill="#f59e0b20" stroke="#f59e0b"/> <path d="M 10 75 H 20 M 15 70 V 80" stroke="#f59e0b" stroke-width="2"/> <text x="40" y="78" font-family="sans-serif" font-size="12" fill="#f8fafc">Quantum Computing</text> </g> <!-- Key Properties Table (Bottom Right) --> <g transform="translate(340, 455)"> <text x="0" y="0" font-family="sans-serif" font-weight="700" font-size="14" fill="#94a3b8">CORE PROPERTIES</text> <rect y="10" width="500" height="1" fill="#ffffff15"/> <text x="0" y="35" font-family="monospace" font-size="12" fill="#f8fafc">A(BC) = (AB)C</text> <text x="140" y="35" font-family="sans-serif" font-size="11" fill="#94a3b8">Associative</text> <text x="250" y="35" font-family="monospace" font-size="12" fill="#f8fafc">AI = IA = A</text> <text x="390" y="35" font-family="sans-serif" font-size="11" fill="#94a3b8">Identity</text> <text x="0" y="60" font-family="monospace" font-size="12" fill="#f8fafc">det(AB) = det(A)det(B)</text> <text x="140" y="60" font-family="sans-serif" font-size="11" fill="#94a3b8">Determinant Product</text> </g> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#38bdf8" stroke-width="0.5" opacity="0.3"/> <circle cx="850" cy="50" r="20" fill="none" stroke="#38bdf8" stroke-width="0.5" opacity="0.5"/> <circle cx="850" cy="50" r="5" fill="#38bdf8" opacity="0.8"/> <!-- Markers --> <defs> <marker 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0v560M520 0v560M560 0v560M600 0v560M640 0v560M680 0v560M720 0v560M760 0v560M800 0v560M840 0v560"/> </g> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">PROBABILITY &amp; COMBINATORICS</text> <text x="450" y="85" text-anchor="middle" font-family="system-ui, sans-serif" font-size="14" fill="#94a3b8" font-style="italic">The Mathematical Science of Uncertainty and Arrangement</text> <rect x="350" y="95" width="200" height="2" fill="url(#accent-orange)" rx="1"/> <!-- Main Panels --> <!-- Left Side: Combinatorics --> <rect x="40" y="120" width="400" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="65" y="155" font-family="system-ui, sans-serif" font-weight="700" font-size="20" fill="#f59e0b">Combinatorics</text> <text x="65" y="175" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8">The Art of Counting without Counting</text> <!-- Permutation Sub-card --> <rect x="60" y="200" width="360" height="135" rx="12" fill="#ffffff05"/> <text x="80" y="225" font-family="system-ui, sans-serif" font-weight="600" font-size="15" fill="#f8fafc">Permutations (Order Matters)</text> <text x="80" y="245" font-family="system-ui, sans-serif" font-size="12" fill="#cbd5e1">Arranging items in a specific sequence.</text> <text x="80" y="275" font-family="serif" font-size="18" fill="#e879f9" font-weight="bold">P(n, r) = n! / (n - r)!</text> <!-- Permutation Icon --> <g transform="translate(340, 240)"> <circle cx="0" cy="0" r="8" fill="#e879f9"/> <circle cx="25" cy="0" r="8" fill="#38bdf8"/> <circle cx="50" cy="0" r="8" fill="#f59e0b"/> <path d="M0 15 L50 15" stroke="#ffffff30" stroke-width="1" marker-end="url(#arrow)"/> <text x="25" y="35" text-anchor="middle" font-size="10" fill="#94a3b8" font-family="system-ui">Sequence</text> </g> <!-- Combination Sub-card --> <rect x="60" y="350" width="360" height="135" rx="12" fill="#ffffff05"/> <text x="80" y="375" font-family="system-ui, sans-serif" font-weight="600" font-size="15" fill="#f8fafc">Combinations (Order Doesn't Matter)</text> <text x="80" y="395" font-family="system-ui, sans-serif" font-size="12" fill="#cbd5e1">Selecting a group where sequence is irrelevant.</text> <text x="80" y="425" font-family="serif" font-size="18" fill="#38bdf8" font-weight="bold">C(n, r) = n! / [r!(n - r)!]</text> <!-- Combination Icon --> <g transform="translate(340, 390)"> <circle cx="10" cy="5" r="8" fill="#e879f9" opacity="0.8"/> <circle cx="35" cy="15" r="8" fill="#38bdf8" opacity="0.8"/> <circle cx="20" cy="30" r="8" fill="#f59e0b" opacity="0.8"/> <circle cx="22" cy="17" r="25" fill="none" stroke="#ffffff40" stroke-dasharray="2 2"/> <text x="22" y="55" text-anchor="middle" font-size="10" fill="#94a3b8" font-family="system-ui">Set/Group</text> </g> <!-- Right Side: Probability --> <rect x="460" y="120" width="400" height="400" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="485" y="155" font-family="system-ui, sans-serif" font-weight="700" font-size="20" fill="#38bdf8">Probability</text> <text x="485" y="175" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8">The Measure of Likelihood</text> <!-- Probability Rule 1 --> <rect x="480" y="200" width="360" height="135" rx="12" fill="#ffffff05"/> <text x="500" y="225" font-family="system-ui, sans-serif" font-weight="600" font-size="15" fill="#f8fafc">Addition Rule (OR Logic)</text> <text x="500" y="245" font-family="system-ui, sans-serif" font-size="12" fill="#cbd5e1">Probability of A or B occurring.</text> <text x="500" y="275" font-family="serif" font-size="16" fill="#f59e0b" font-weight="bold">P(A ∪ B) = P(A) + P(B) - P(A ∩ B)</text> <!-- Venn Icon --> <g transform="translate(760, 240)"> <circle cx="0" cy="0" r="20" fill="#f59e0b" opacity="0.4"/> <circle cx="25" cy="0" r="20" fill="#38bdf8" opacity="0.4"/> <text x="12" y="35" text-anchor="middle" font-size="10" fill="#94a3b8" font-family="system-ui">Inclusion-Exclusion</text> </g> <!-- Probability Rule 2 --> <rect x="480" y="350" width="360" height="135" rx="12" fill="#ffffff05"/> <text x="500" y="375" font-family="system-ui, sans-serif" font-weight="600" font-size="15" fill="#f8fafc">Multiplication Rule (AND Logic)</text> <text x="500" y="395" font-family="system-ui, sans-serif" font-size="12" fill="#cbd5e1">Probability of A and B occurring together.</text> <text x="500" y="425" font-family="serif" font-size="16" fill="#e879f9" font-weight="bold">P(A ∩ B) = P(A) × P(B|A)</text> <!-- Tree Icon --> <g transform="translate(760, 385)"> <line x1="0" y1="20" x2="20" y2="0" stroke="#ffffff40" stroke-width="2"/> <line x1="0" y1="20" x2="20" y2="40" stroke="#ffffff40" stroke-width="2"/> <circle cx="20" cy="0" r="5" fill="#e879f9"/> <circle cx="20" cy="40" r="5" fill="#38bdf8"/> <text x="10" y="55" text-anchor="middle" font-size="10" fill="#94a3b8" font-family="system-ui">Branching Events</text> </g> <!-- Central Connection --> <circle cx="450" cy="320" r="25" fill="#1e1b4b" stroke="#ffffff20" stroke-width="2"/> <path d="M440 310 L460 330 M460 310 L440 330" stroke="#f59e0b" stroke-width="3" stroke-linecap="round"/> <!-- Bottom Fact Bar --> <rect x="40" y="530" width="820" height="20" rx="4" fill="#ffffff05"/> <text x="450" y="544" text-anchor="middle" font-family="system-ui, sans-serif" font-size="10" fill="#64748b" text-transform="uppercase" letter-spacing="2">Fundamental Principle: If task A has n ways and B has m ways, then A then B has n × m ways.</text> <!-- Decorative Corner Elements --> <circle cx="20" cy="20" r="3" fill="#f59e0b" opacity="0.5"/> <circle cx="880" cy="20" r="3" fill="#38bdf8" opacity="0.5"/> <circle cx="20" cy="540" r="3" fill="#e879f9" opacity="0.5"/> <circle cx="880" cy="540" r="3" fill="#f59e0b" opacity="0.5"/> </svg>Probability and Combinatorics image 1Probability and Combinatorics - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/probability-and-combinatorics/svg/1Probability and Combinatorics diagram 1Probability and Combinatorics - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/probability-and-combinatorics/svg/2Probability and Combinatorics diagram 2Probability and Combinatorics - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Background and Definitions --> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" x="0" y="0" width="30" height="30" patternUnits="userSpaceOnUse"> <path d="M 30 0 L 0 0 0 30" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Base Layers --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1px">SERIES &amp; THE BINOMIAL THEOREM</text> <path d="M 350 65 L 550 65" stroke="#38bdf8" stroke-width="2" stroke-linecap="round" opacity="0.6"/> <text x="450" y="85" text-anchor="middle" font-family="system-ui, sans-serif" font-size="14" fill="#94a3b8" font-style="italic">The Bridge Between Discrete Steps and Infinite Sums</text> <!-- Section 1: Sigma Notation (Top Left) --> <rect x="40" y="110" width="260" height="150" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="140" font-family="system-ui, sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">Σ Notation</text> <!-- Sigma Graphic --> <g transform="translate(140, 160)"> <path d="M 0 0 L 40 0 L 15 25 L 40 50 L 0 50" fill="none" stroke="#f8fafc" stroke-width="4" stroke-linejoin="round"/> <text x="20" y="-10" text-anchor="middle" font-family="serif" font-size="14" fill="#f59e0b">n</text> <text x="20" y="65" text-anchor="middle" font-family="serif" font-size="14" fill="#f59e0b">i = k</text> <text x="50" y="32" font-family="serif" font-size="20" fill="#f8fafc">aᵢ</text> <!-- Labels --> <text x="-70" y="30" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">SUMMATION</text> <line x1="-5" y1="-15" x2="10" y2="-15" stroke="#94a3b8" stroke-width="1"/> <text x="-70" y="-12" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">UPPER LIMIT</text> </g> <!-- Section 2: Binomial Theorem (Top Right) --> <rect x="320" y="110" width="540" height="150" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="340" y="140" font-family="system-ui, sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">The Binomial Theorem</text> <text x="340" y="170" font-family="serif" font-size="22" fill="#f8fafc">(a + b)ⁿ = Σ <tspan fill="#f59e0b">ⁿCₖ</tspan> aⁿ⁻ᵏ bᵏ</text> <!-- Pascal's Triangle Visual --> <g transform="translate(680, 135)" opacity="0.8"> <text x="0" y="0" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">1</text> <text x="-15" y="20" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">1</text> <text x="15" y="20" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">1</text> <text x="-30" y="40" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">1</text> <text x="0" y="40" text-anchor="middle" font-family="serif" font-size="12" fill="#f59e0b" font-weight="bold">2</text> <text x="30" y="40" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">1</text> <text x="-45" y="60" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">1</text> <text x="-15" y="60" text-anchor="middle" font-family="serif" font-size="12" fill="#f59e0b" font-weight="bold">3</text> <text x="15" y="60" text-anchor="middle" font-family="serif" font-size="12" fill="#f59e0b" font-weight="bold">3</text> <text x="45" y="60" text-anchor="middle" font-family="serif" font-size="12" fill="#94a3b8">1</text> <text x="0" y="85" text-anchor="middle" font-family="system-ui, sans-serif" font-size="10" fill="#f59e0b">PASCAL'S TRIANGLE</text> </g> <!-- Section 3: Arithmetic Series (Bottom Left) --> <rect x="40" y="280" width="400" height="240" rx="16" fill="#ffffff0a" stroke="#38bdf844"/> <text x="60" y="315" font-family="system-ui, sans-serif" font-weight="bold" font-size="20" fill="#38bdf8">Arithmetic Series</text> <text x="60" y="335" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8">Constant difference (d) | Linear Growth</text> <!-- Formula --> <rect x="60" y="350" width="180" height="45" rx="8" fill="#38bdf815"/> <text x="75" y="380" font-family="serif" font-size="18" fill="#f8fafc">Sₙ = ⁿ/₂ (a₁ + aₙ)</text> <!-- Gauss Visualization --> <g transform="translate(60, 420)"> <rect x="0" y="40" width="20" height="20" fill="#38bdf8" opacity="0.4"/> <rect x="25" y="30" width="20" height="30" fill="#38bdf8" opacity="0.5"/> <rect x="50" y="20" width="20" height="40" fill="#38bdf8" opacity="0.7"/> <rect x="75" y="10" width="20" height="50" fill="#38bdf8" opacity="0.9"/> <rect x="100" y="0" width="20" height="60" fill="#38bdf8"/> <text x="0" y="80" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Gauss's Trick: Pairing terms</text> </g> <!-- Section 4: Geometric Series (Bottom Right) --> <rect x="460" y="280" width="400" height="240" rx="16" fill="#ffffff0a" stroke="#e879f944"/> <text x="480" y="315" font-family="system-ui, sans-serif" font-weight="bold" font-size="20" fill="#e879f9">Geometric Series</text> <text x="480" y="335" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8">Common ratio (r) | Exponential Growth</text> <!-- Formula --> <rect x="480" y="350" width="180" height="45" rx="8" fill="#e879f915"/> <text x="495" y="380" font-family="serif" font-size="18" fill="#f8fafc">S = a₁ / (1 - r)</text> <text x="670" y="378" font-family="system-ui, sans-serif" font-size="11" fill="#e879f9" font-weight="bold">IF |r| &lt; 1</text> <!-- Convergence Visualization --> <g transform="translate(480, 420)"> <rect x="0" y="0" width="60" height="60" fill="#e879f9" opacity="0.8"/> <rect x="60" y="0" width="30" height="60" fill="#e879f9" opacity="0.6"/> <rect x="90" y="0" width="15" height="60" fill="#e879f9" opacity="0.4"/> <rect x="105" y="0" width="7.5" height="60" fill="#e879f9" opacity="0.2"/> <path d="M 0 65 L 120 65" stroke="#94a3b8" stroke-dasharray="4 2"/> <text x="0" y="80" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Convergence: Approaching a limit</text> </g> <!-- Applications Footer --> <g transform="translate(40, 535)"> <text x="0" y="0" font-family="system-ui, sans-serif" font-size="10" font-weight="bold" fill="#38bdf8" letter-spacing="1px">APPLICATIONS:</text> <text x="100" y="0" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">FINANCE (Annuities)</text> <circle cx="210" cy="-3" r="2" fill="#ffffff33"/> <text x="225" y="0" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">PHYSICS (Wave Harmonics)</text> <circle cx="370" cy="-3" r="2" fill="#ffffff33"/> <text x="385" y="0" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">COMP. SCI (Complexity Analysis)</text> </g> </svg>Series and Binomial Theorem image 1Series and Binomial Theorem - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/series-and-binomial-theorem/svg/1Series and Binomial Theorem diagram 1Series and Binomial Theorem - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/series-and-binomial-theorem/svg/2Series and Binomial Theorem diagram 2Series and Binomial Theorem - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Background and Definitions --> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="30" height="30" patternUnits="userSpaceOnUse"> <circle cx="1" cy="1" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Base Layer --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="40" y="60" font-family="system-ui, sans-serif" font-weight="800" font-size="32" fill="#f8fafc">LIMITS &amp; CONTINUITY</text> <text x="40" y="85" font-family="system-ui, sans-serif" font-size="16" fill="#94a3b8">The rigorous foundation of modern Calculus</text> <rect x="40" y="105" width="120" height="4" rx="2" fill="#38bdf8"/> <!-- Left Column: The Limit Concept --> <rect x="40" y="130" width="260" height="390" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="165" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#38bdf8">I. THE LIMIT</text> <text x="60" y="185" font-family="system-ui, sans-serif" font-size="13" fill="#cbd5e1">Behavior near a point, not at it.</text> <!-- Limit Diagram --> <g transform="translate(60, 210)"> <path d="M 0 100 Q 50 80 100 20 T 200 0" fill="none" stroke="#38bdf8" stroke-width="3"/> <circle cx="100" cy="20" r="5" fill="none" stroke="#38bdf8" stroke-width="2"/> <path d="M 80 20 L 92 20" stroke="#f59e0b" stroke-width="2" marker-end="url(#arrow)"/> <path d="M 120 20 L 108 20" stroke="#f59e0b" stroke-width="2"/> <text x="105" y="45" font-family="serif" font-style="italic" font-size="14" fill="#f8fafc">L</text> <text x="95" y="115" font-family="serif" font-style="italic" font-size="14" fill="#f8fafc">c</text> <line x1="0" y1="100" x2="220" y2="100" stroke="#94a3b8" stroke-dasharray="4"/> </g> <text x="60" y="345" font-family="system-ui, sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Formal Definition (ε-δ)</text> <rect x="60" y="355" width="220" height="145" rx="8" fill="#ffffff05"/> <text x="70" y="380" font-family="serif" font-size="13" fill="#94a3b8">For every ε &gt; 0, there exists</text> <text x="70" y="398" font-family="serif" font-size="13" fill="#94a3b8">a δ &gt; 0 such that:</text> <text x="70" y="425" font-family="serif" font-weight="bold" font-size="15" fill="#f59e0b">0 &lt; |x - c| &lt; δ</text> <text x="70" y="445" font-family="serif" font-size="13" fill="#94a3b8">implies</text> <text x="70" y="472" font-family="serif" font-weight="bold" font-size="15" fill="#e879f9">|f(x) - L| &lt; ε</text> <!-- Middle Column: Continuity --> <rect x="320" y="130" width="260" height="390" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="340" y="165" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#e879f9">II. CONTINUITY</text> <text x="340" y="185" font-family="system-ui, sans-serif" font-size="13" fill="#cbd5e1">The "Unbroken Path" test.</text> <!-- Continuity Checklist --> <g transform="translate(340, 220)"> <rect width="220" height="40" rx="8" fill="#38bdf820"/> <circle cx="20" cy="20" r="8" fill="#38bdf8"/> <text x="16" y="24" font-family="sans-serif" font-size="10" font-weight="bold" fill="#0f172a">1</text> <text x="40" y="25" font-family="serif" font-size="14" fill="#f8fafc">f(c) is defined</text> <rect y="55" width="220" height="40" rx="8" fill="#f59e0b20"/> <circle cx="20" cy="75" r="8" fill="#f59e0b"/> <text x="16" y="79" font-family="sans-serif" font-size="10" font-weight="bold" fill="#0f172a">2</text> <text x="40" y="80" font-family="serif" font-size="14" fill="#f8fafc">lim f(x) exists</text> <rect y="110" width="220" height="40" rx="8" fill="#e879f920"/> <circle cx="20" cy="130" r="8" fill="#e879f9"/> <text x="16" y="134" font-family="sans-serif" font-size="10" font-weight="bold" fill="#0f172a">3</text> <text x="40" y="135" font-family="serif" font-size="14" fill="#f8fafc">lim f(x) = f(c)</text> </g> <text x="340" y="400" font-family="system-ui, sans-serif" font-size="12" fill="#94a3b8" width="220"> <tspan x="340" dy="1.4em">A function is continuous on an</tspan> <tspan x="340" dy="1.4em">interval if it is continuous at</tspan> <tspan x="340" dy="1.4em">every point in that interval.</tspan> </text> <path d="M 340 470 Q 450 440 540 500" fill="none" stroke="#e879f9" stroke-width="4" stroke-linecap="round" filter="url(#glow)"/> <!-- Right Column: Discontinuities --> <rect x="600" y="130" width="260" height="390" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="165" font-family="system-ui, sans-serif" font-weight="700" font-size="18" fill="#f59e0b">III. DISCONTINUITIES</text> <!-- Discontinuity Type 1 --> <g transform="translate(620, 200)"> <text x="0" y="0" font-family="system-ui, sans-serif" font-weight="bold" font-size="12" fill="#f8fafc">REMOVABLE (HOLE)</text> <path d="M 0 40 Q 40 20 80 40" fill="none" stroke="#94a3b8" stroke-width="2"/> <circle cx="40" cy="30" r="4" fill="#0f172a" stroke="#f59e0b" stroke-width="2"/> <text x="90" y="35" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Limit exists,</text> <text x="90" y="48" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">point is missing.</text> </g> <!-- Discontinuity Type 2 --> <g transform="translate(620, 290)"> <text x="0" y="0" font-family="system-ui, sans-serif" font-weight="bold" font-size="12" fill="#f8fafc">JUMP</text> <path d="M 0 40 L 40 40" fill="none" stroke="#94a3b8" stroke-width="2"/> <path d="M 40 20 L 80 20" fill="none" stroke="#94a3b8" stroke-width="2"/> <circle cx="40" cy="40" r="3" fill="#f59e0b"/> <circle cx="40" cy="20" r="3" fill="none" stroke="#f59e0b" stroke-width="1.5"/> <text x="90" y="25" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Left limit ≠</text> <text x="90" y="38" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Right limit.</text> </g> <!-- Discontinuity Type 3 --> <g transform="translate(620, 380)"> <text x="0" y="0" font-family="system-ui, sans-serif" font-weight="bold" font-size="12" fill="#f8fafc">INFINITE (ASYMPTOTE)</text> <line x1="40" y1="10" x2="40" y2="70" stroke="#f59e0b" stroke-dasharray="3"/> <path d="M 10 70 Q 15 20 35 15" fill="none" stroke="#94a3b8" stroke-width="2"/> <path d="M 70 70 Q 65 20 45 15" fill="none" stroke="#94a3b8" stroke-width="2"/> <text x="90" y="35" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Approaches</text> <text x="90" y="48" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">± Infinity.</text> </g> <!-- Footer Stats/Facts --> <rect x="620" y="475" width="220" height="30" rx="15" fill="#38bdf815"/> <text x="730" y="495" text-anchor="middle" font-family="system-ui, sans-serif" font-weight="bold" font-size="12" fill="#38bdf8">SQUEEZE THEOREM: g(x) ≤ f(x) ≤ h(x)</text> <!-- Decorative Elements --> <circle cx="850" cy="50" r="30" fill="#e879f910"/> <circle cx="850" cy="50" r="15" fill="#e879f920"/> <path d="M 830 50 L 870 50 M 850 30 L 850 70" stroke="#e879f940" stroke-width="1"/> </svg>Limits and Continuity image 1Limits and Continuity - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/limits-and-continuity/svg/1Limits and Continuity diagram 1Limits and Continuity - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/limits-and-continuity/svg/2Limits and Continuity diagram 2Limits and Continuity - Precalculus - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Decorative Background Elements --> <circle cx="850" cy="50" r="120" fill="#38bdf805"/> <circle cx="50" cy="510" r="80" fill="#e879f905"/> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="2">PRECALCULUS COURSE CHALLENGE</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-weight="400" font-size="14" fill="#94a3b8" letter-spacing="1">A RIGOROUS SYNTHESIS OF ALGEBRAIC &amp; TRIGONOMETRIC MASTERY</text> <rect x="350" y="95" width="200" height="4" rx="2" fill="url(#accentGrad)"/> <!-- Left Column: Technical Engine --> <rect x="40" y="120" width="260" height="400" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="60" y="155" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">SYSTEM ENGINE</text> <!-- JS Icon --> <rect x="60" y="175" width="40" height="40" rx="8" fill="#38bdf820"/> <path d="M 72 187 L 68 195 L 72 203 M 88 187 L 92 195 L 88 203" stroke="#38bdf8" stroke-width="2" fill="none"/> <text x="110" y="190" font-family="sans-serif" font-weight="600" font-size="14" fill="#f8fafc">JavaScript Required</text> <text x="110" y="205" font-family="sans-serif" font-size="11" fill="#94a3b8">Client-side logic engine</text> <g transform="translate(60, 235)"> <circle cx="15" cy="15" r="15" fill="#ffffff08"/> <path d="M 10 15 L 20 15 M 15 10 L 15 20" stroke="#94a3b8" stroke-width="2"/> <text x="40" y="12" font-family="sans-serif" font-weight="600" font-size="13" fill="#f8fafc">State Management</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Real-time progress tracking</text> </g> <g transform="translate(60, 285)"> <circle cx="15" cy="15" r="15" fill="#ffffff08"/> <path d="M 10 12 L 20 12 M 10 18 L 20 18" stroke="#94a3b8" stroke-width="2"/> <text x="40" y="12" font-family="sans-serif" font-weight="600" font-size="13" fill="#f8fafc">Dynamic Rendering</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">LaTeX &amp; MathJax integration</text> </g> <g transform="translate(60, 335)"> <circle cx="15" cy="15" r="15" fill="#ffffff08"/> <path d="M 8 22 L 15 8 L 22 22" stroke="#94a3b8" stroke-width="2" fill="none"/> <text x="40" y="12" font-family="sans-serif" font-weight="600" font-size="13" fill="#f8fafc">Interactive Graphing</text> <text x="40" y="26" font-family="sans-serif" font-size="11" fill="#94a3b8">Embedded visualization tools</text> </g> <!-- Center Column: Mastery Metric --> <rect x="320" y="120" width="260" height="400" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="450" y="155" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">MASTERY METRIC</text> <!-- Mastery Gauge --> <circle cx="450" cy="240" r="60" fill="none" stroke="#ffffff10" stroke-width="12"/> <path d="M 450 180 A 60 60 0 1 1 398 210" fill="none" stroke="#f59e0b" stroke-width="12" stroke-linecap="round"/> <text x="450" y="235" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="24" fill="#f8fafc">100%</text> <text x="450" y="255" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#94a3b8">PROFICIENCY</text> <rect x="350" y="320" width="200" height="160" rx="12" fill="#00000020"/> <text x="450" y="345" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">EXAM STRUCTURE</text> <text x="370" y="375" font-family="sans-serif" font-size="12" fill="#94a3b8">Questions:</text> <text x="530" y="375" text-anchor="end" font-family="sans-serif" font-weight="700" font-size="12" fill="#f8fafc">30 Items</text> <text x="370" y="400" font-family="sans-serif" font-size="12" fill="#94a3b8">Sampling:</text> <text x="530" y="400" text-anchor="end" font-family="sans-serif" font-weight="700" font-size="12" fill="#f8fafc">Stochastic</text> <text x="370" y="425" font-family="sans-serif" font-size="12" fill="#94a3b8">Skill Units:</text> <text x="530" y="425" text-anchor="end" font-family="sans-serif" font-weight="700" font-size="12" fill="#f8fafc">10 Primary</text> <text x="370" y="450" font-family="sans-serif" font-size="12" fill="#94a3b8">Total Points:</text> <text x="530" y="450" text-anchor="end" font-family="sans-serif" font-weight="700" font-size="12" fill="#f8fafc">Thousands</text> <!-- Right Column: Core Competencies --> <rect x="600" y="120" width="260" height="400" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <text x="620" y="155" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">CORE DOMAINS</text> <!-- Domain 1 --> <g transform="translate(620, 180)"> <text x="0" y="0" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">1. Functions &amp; Inverses</text> <path d="M 0 15 Q 25 5 50 25" stroke="#e879f9" stroke-width="2" fill="none"/> <line x1="0" y1="20" x2="50" y2="20" stroke="#ffffff30" stroke-dasharray="2,2"/> <text x="60" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">Horizontal Line Test</text> </g> <!-- Domain 2 --> <g transform="translate(620, 260)"> <text x="0" y="0" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">2. Sinusoidal Modeling</text> <path d="M 0 20 Q 12.5 0 25 20 T 50 20" stroke="#e879f9" stroke-width="2" fill="none"/> <text x="60" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">y = A sin(B(x-C)) + D</text> </g> <!-- Domain 3 --> <g transform="translate(620, 340)"> <text x="0" y="0" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">3. Rational Functions</text> <path d="M 5 5 Q 15 15 15 40 M 35 0 Q 35 25 45 35" stroke="#e879f9" stroke-width="2" fill="none"/> <line x1="25" y1="0" x2="25" y2="40" stroke="#ffffff30" stroke-dasharray="2,2"/> <text x="60" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">Asymptotic Behavior</text> </g> <!-- Domain 4 --> <g transform="translate(620, 420)"> <text x="0" y="0" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">4. Vectors &amp; Matrices</text> <path d="M 0 30 L 40 10 M 35 10 L 40 10 L 40 15" stroke="#e879f9" stroke-width="2" fill="none"/> <text x="60" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">Linear Transformations</text> </g> <!-- Footer --> <text x="450" y="545" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#475569" letter-spacing="1">PRECALCULUS CURRICULUM • DIAGNOSTIC ENGINE v2.4 • MASTERY-BASED ASSESSMENT</text> </svg>Precalculus Course Challenge image 1Precalculus Course Challenge - Precalculus - image 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/course-challenge/svg/1Precalculus Course Challenge diagram 1Precalculus Course Challenge - Precalculus - diagram 1https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/course-challenge/svg/2Precalculus Course Challenge diagram 2Precalculus Course Challenge - Precalculus - diagram 2https://www.getlykke.com/explore/public/precalculus-760426f2-c765-4f63-848e-73deae621c37/media/course-challenge/svg/3Precalculus Course Challenge diagram 3Precalculus Course Challenge - Precalculus - diagram 3https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba82026-04-20T04:49:11.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background Layer --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Decorative Background Elements --> <circle cx="850" cy="50" r="120" fill="#38bdf8" fill-opacity="0.05"/> <circle cx="50" cy="510" r="100" fill="#e879f9" fill-opacity="0.05"/> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="1">THE SPECTRUM OF COMPUTATION</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="400" fill="#94a3b8" text-transform="uppercase" letter-spacing="4">From Mathematical Theory to Machine Execution</text> <rect x="400" y="95" width="100" height="4" rx="2" fill="url(#accentGrad)"/> <!-- Left Column: Computer Science (The Physics) --> <g transform="translate(40, 130)"> <rect width="260" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <rect x="20" y="20" width="40" height="40" rx="8" fill="#38bdf820"/> <path d="M 30 40 L 40 30 L 50 40 L 40 50 Z" fill="none" stroke="#38bdf8" stroke-width="2"/> <circle cx="40" cy="40" r="3" fill="#38bdf8"/> <text x="75" y="38" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">Computer Science</text> <text x="75" y="55" font-family="sans-serif" font-size="12" font-weight="400" fill="#94a3b8">The Theoretical Foundation</text> <text x="20" y="95" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Core Question:</text> <text x="20" y="115" font-family="sans-serif" font-size="13" font-style="italic" fill="#cbd5e1">"What is computable?"</text> <g transform="translate(20, 145)"> <circle cx="5" cy="5" r="3" fill="#38bdf8"/> <text x="15" y="9" font-family="sans-serif" font-size="12" fill="#94a3b8">Algorithm Complexity (Big O)</text> <circle cx="5" cy="25" r="3" fill="#38bdf8"/> <text x="15" y="29" font-family="sans-serif" font-size="12" fill="#94a3b8">Data Structures &amp; Logic</text> <circle cx="5" cy="45" r="3" fill="#38bdf8"/> <text x="15" y="49" font-family="sans-serif" font-size="12" fill="#94a3b8">Information Theory</text> </g> <path d="M 40 230 Q 130 210 220 230" fill="none" stroke="#ffffff10" stroke-width="2" stroke-dasharray="4 4"/> <text x="130" y="270" text-anchor="middle" font-family="serif" font-size="36" fill="#ffffff05">f(x)</text> </g> <!-- Middle Column: Programming (The Bridge) --> <g transform="translate(320, 130)"> <rect width="260" height="320" rx="16" fill="#ffffff12" stroke="#ffffff20" stroke-width="1.5"/> <rect x="20" y="20" width="40" height="40" rx="8" fill="#f59e0b20"/> <path d="M 30 35 L 50 35 M 30 45 L 50 45 M 40 30 L 40 50" fill="none" stroke="#f59e0b" stroke-width="2"/> <text x="75" y="38" font-family="sans-serif" font-size="18" font-weight="700" fill="#f59e0b">Programming</text> <text x="75" y="55" font-family="sans-serif" font-size="12" font-weight="400" fill="#94a3b8">The Applied Craft</text> <text x="20" y="95" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Core Question:</text> <text x="20" y="115" font-family="sans-serif" font-size="13" font-style="italic" fill="#cbd5e1">"How do we build the solution?"</text> <g transform="translate(20, 145)"> <rect x="0" y="0" width="220" height="110" rx="8" fill="#00000020"/> <text x="10" y="20" font-family="monospace" font-size="11" fill="#f59e0b">1. Problem Analysis</text> <text x="10" y="40" font-family="monospace" font-size="11" fill="#f8fafc">2. Algorithm Design</text> <text x="10" y="60" font-family="monospace" font-size="11" fill="#f8fafc">3. Implementation</text> <text x="10" y="80" font-family="monospace" font-size="11" fill="#f8fafc">4. Testing &amp; Debugging</text> <text x="10" y="100" font-family="monospace" font-size="11" fill="#94a3b8">5. Maintenance</text> </g> </g> <!-- Right Column: Coding (The Bricks) --> <g transform="translate(600, 130)"> <rect width="260" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <rect x="20" y="20" width="40" height="40" rx="8" fill="#e879f920"/> <path d="M 32 35 L 38 40 L 32 45 M 48 35 L 42 40 L 48 45" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="75" y="38" font-family="sans-serif" font-size="18" font-weight="700" fill="#e879f9">Coding</text> <text x="75" y="55" font-family="sans-serif" font-size="12" font-weight="400" fill="#94a3b8">The Translation Layer</text> <text x="20" y="95" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Core Question:</text> <text x="20" y="115" font-family="sans-serif" font-size="13" font-style="italic" fill="#cbd5e1">"How do I write the syntax?"</text> <g transform="translate(20, 145)"> <text x="0" y="15" font-family="sans-serif" font-size="12" fill="#94a3b8">Translating logic into</text> <text x="0" y="32" font-family="sans-serif" font-size="12" fill="#94a3b8">executable instructions.</text> <rect x="0" y="50" width="220" height="80" rx="8" fill="#00000040"/> <text x="10" y="70" font-family="monospace" font-size="11" fill="#38bdf8">while</text> <text x="55" y="70" font-family="monospace" font-size="11" fill="#f8fafc">(data &gt; 0) {</text> <text x="25" y="90" font-family="monospace" font-size="11" fill="#e879f9">process</text> <text x="75" y="90" font-family="monospace" font-size="11" fill="#f8fafc">(data--);</text> <text x="10" y="110" font-family="monospace" font-size="11" fill="#f8fafc">}</text> </g> </g> <!-- Bottom Section: The Bridge (Compilers) --> <g transform="translate(40, 470)"> <rect width="820" height="70" rx="12" fill="#ffffff05" stroke="#ffffff10"/> <text x="20" y="40" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">THE TRANSLATORS</text> <g transform="translate(160, 20)"> <text x="0" y="15" font-family="monospace" font-size="12" fill="#94a3b8">Source Code</text> <path d="M 85 10 L 125 10" stroke="#38bdf8" stroke-width="2" marker-end="url(#arrow)"/> <rect x="140" y="-5" width="160" height="30" rx="6" fill="#38bdf820" stroke="#38bdf8"/> <text x="220" y="15" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">COMPILER / INTERPRETER</text> <path d="M 315 10 L 355 10" stroke="#e879f9" stroke-width="2"/> <text x="370" y="15" font-family="monospace" font-size="12" fill="#e879f9">Machine Code (010110...)</text> </g> </g> <!-- Connection Arrows --> <defs> <marker id="arrow" markerWidth="10" markerHeight="10" refX="9" refY="5" orientation="auto"> <path d="M0,0 L10,5 L0,10 Z" fill="#ffffff30" /> </marker> </defs> <path d="M 300 290 L 320 290" stroke="#ffffff20" stroke-width="2" marker-end="url(#arrow)"/> <path d="M 580 290 L 600 290" stroke="#ffffff20" stroke-width="2" marker-end="url(#arrow)"/> </svg>Introduction to Computer Science and Programming image 1Introduction to Computer Science and Programming - Intro to Python Fundamentals - image 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/introduction-to-computer-science/svg/1Introduction to Computer Science and Programming diagram 1Introduction to Computer Science and Programming - Intro to Python Fundamentals - diagram 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/introduction-to-computer-science/svg/2Introduction to Computer Science and Programming diagram 2Introduction to Computer Science and Programming - Intro to Python Fundamentals - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Definitions for Gradients and Filters --> <defs> <linearGradient id="bgGradient" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="blueGrad" x1="0" y1="0" 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ENGINE</text> <text x="60" y="180" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">JavaScript Prerequisite</text> <text x="60" y="200" font-family="sans-serif" font-size="12" fill="#94a3b8">The "Glue" of the Browser IDE</text> <g transform="translate(60, 230)"> <rect width="220" height="50" rx="8" fill="#ffffff08"/> <text x="10" y="20" font-family="sans-serif" font-weight="600" font-size="12" fill="#38bdf8">DOM Manipulation</text> <text x="10" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Dynamic UI updates as you type.</text> </g> <g transform="translate(60, 290)"> <rect width="220" height="50" rx="8" fill="#ffffff08"/> <text x="10" y="20" font-family="sans-serif" font-weight="600" font-size="12" fill="#38bdf8">Event Handling</text> <text x="10" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Capturing keystrokes &amp; clicks.</text> </g> <g transform="translate(60, 350)"> <rect width="220" height="50" rx="8" fill="#ffffff08"/> <text x="10" y="20" font-family="sans-serif" font-weight="600" font-size="12" fill="#38bdf8">Client-Side Interpreter</text> <text x="10" y="38" font-family="sans-serif" font-size="11" fill="#94a3b8">Running Python logic locally.</text> </g> <!-- Column 2: The IDE Interface --> <rect x="320" y="100" width="260" height="360" rx="16" fill="url(#pinkGrad)" stroke="#e879f940" stroke-width="1"/> <circle cx="355" cy="135" r="18" fill="#e879f920"/> <path d="M 348 130 L 362 130 M 348 135 L 358 135 M 348 140 L 362 140" fill="none" stroke="#e879f9" stroke-width="2.5"/> <text x="385" y="140" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">THE INTERFACE</text> <text x="340" y="180" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">Code Editor Features</text> <!-- Syntax Highlighting Mockup --> <rect x="340" y="200" width="220" height="100" rx="8" fill="#00000040"/> <rect x="350" y="215" width="40" height="6" rx="3" fill="#e879f9"/> <!-- def --> <rect 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font-size="12" fill="#94a3b8"> <tspan fill="#f59e0b" font-weight="bold">TIP:</tspan> Minimizing "Environmental Friction" allows focus on algorithmic logic and computational thinking. </text> <text x="840" y="520" text-anchor="end" font-family="sans-serif" font-size="11" font-weight="bold" fill="#38bdf8">CLIENT CHALLENGE v2.0</text> </svg>Technical Requirements and the Development Environment image 1Technical Requirements and the Development Environment - Intro to Python Fundamentals - image 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/technical-requirements-and-ide/svg/1Technical Requirements and the Development Environment diagram 1Technical Requirements and the Development Environment - Intro to Python Fundamentals - diagram 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/technical-requirements-and-ide/svg/2Technical Requirements and the Development Environment diagram 2Technical Requirements and the Development Environment - Intro to Python Fundamentals - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background and Grid --> <rect width="900" height="560" fill="url(#bg)"/> <g stroke="#ffffff08" stroke-width="1"> <path d="M0 40h900M0 80h900M0 120h900M0 160h900M0 200h900M0 240h900M0 280h900M0 320h900M0 360h900M0 400h900M0 440h900M0 480h900M0 520h900"/> <path d="M40 0v560M80 0v560M120 0v560M160 0v560M200 0v560M240 0v560M280 0v560M320 0v560M360 0v560M400 0v560M440 0v560M480 0v560M520 0v560M560 0v560M600 0v560M640 0v560M680 0v560M720 0v560M760 0v560M800 0v560M840 0v560"/> </g> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">UNIT 1</text> <text x="155" y="60" font-family="sans-serif" font-weight="300" font-size="32" fill="#94a3b8">/</text> <text x="180" y="60" font-family="sans-serif" font-weight="700" font-size="28" fill="url(#accentGrad)">COMPUTATIONAL THINKING &amp; VARIABLES</text> <rect x="40" y="85" width="820" height="2" fill="url(#accentGrad)" opacity="0.5"/> <!-- Left Column: Sequence & State --> <rect x="40" y="110" width="400" height="220" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="140" font-family="sans-serif" font-weight="bold" font-size="18" fill="#38bdf8">01. THE CORE MECHANICS</text> <!-- Sequence Visual --> <g transform="translate(60, 160)"> <rect width="110" height="40" rx="8" fill="#38bdf820" stroke="#38bdf8" stroke-width="1"/> <text x="55" y="25" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">SEQUENCE</text> <path d="M110 20 L130 20" stroke="#94a3b8" stroke-width="2" marker-end="url(#arrow)"/> <rect x="140" width="110" height="40" rx="8" fill="#e879f920" stroke="#e879f9" stroke-width="1"/> <text x="195" y="25" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#e879f9">TRANSITION</text> <path d="M250 20 L270 20" stroke="#94a3b8" stroke-width="2"/> <rect x="280" width="100" height="40" rx="8" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1"/> <text x="330" y="25" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f59e0b">STATE</text> </g> <text x="60" y="235" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="bold">Sequence: <tspan font-weight="normal" fill="#94a3b8">The deterministic path of instructions.</tspan></text> <text x="60" y="255" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="bold">State: <tspan font-weight="normal" fill="#94a3b8">The snapshot of memory at time </tspan><tspan font-style="italic" fill="#e879f9">t</tspan><tspan font-weight="normal" fill="#94a3b8">.</tspan></text> <path d="M60 280 L380 280" stroke="#ffffff10" stroke-width="1"/> <text x="60" y="305" font-family="sans-serif" font-size="11" fill="#94a3b8" font-style="italic">"A change in sequence fundamentally alters the outcome."</text> <!-- Right Column: Binary Data --> <rect x="460" y="110" width="400" height="220" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="480" y="140" font-family="sans-serif" font-weight="bold" font-size="18" fill="#f59e0b">02. BINARY ATOMICS</text> <!-- Binary Visual --> <g transform="translate(480, 160)"> <rect x="0" y="0" width="30" height="40" rx="4" fill="#f59e0b" opacity="0.8"/> <text x="15" y="25" text-anchor="middle" font-family="monospace" font-size="18" font-weight="bold" fill="#0f172a">1</text> <rect x="35" y="0" width="30" height="40" rx="4" fill="#ffffff10" stroke="#f59e0b"/> <text x="50" y="25" text-anchor="middle" font-family="monospace" font-size="18" font-weight="bold" fill="#f8fafc">0</text> <rect x="70" y="0" width="30" height="40" rx="4" fill="#f59e0b" opacity="0.8"/> <text x="85" y="25" text-anchor="middle" font-family="monospace" font-size="18" font-weight="bold" fill="#0f172a">1</text> <rect x="105" y="0" width="30" height="40" rx="4" fill="#f59e0b" opacity="0.8"/> <text x="120" y="25" text-anchor="middle" font-family="monospace" font-size="18" font-weight="bold" fill="#0f172a">1</text> <text x="150" y="25" font-family="sans-serif" font-size="14" fill="#94a3b8">=</text> <text x="175" y="25" font-family="sans-serif" font-size="22" font-weight="bold" fill="#f8fafc">11</text> <text x="205" y="25" font-family="sans-serif" font-size="12" fill="#94a3b8">(Decimal)</text> </g> <text x="480" y="235" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="bold">Bit: <tspan font-weight="normal" fill="#94a3b8">Smallest unit (0 or 1).</tspan></text> <text x="480" y="255" font-family="sans-serif" font-size="13" fill="#f8fafc" font-weight="bold">Byte: <tspan font-weight="normal" fill="#94a3b8">8 bits (256 distinct values).</tspan></text> <g transform="translate(480, 280)"> <rect width="360" height="35" rx="8" fill="#00000030"/> <text x="10" y="22" font-family="serif" font-size="14" fill="#38bdf8" font-style="italic">Value = Σ (d_i × 2^i)</text> <text x="160" y="22" font-family="sans-serif" font-size="11" fill="#94a3b8">Positional notation derivation</text> </g> <!-- Bottom Section: Data Types --> <rect x="40" y="350" width="820" height="170" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="385" font-family="sans-serif" font-weight="bold" font-size="18" fill="#e879f9">03. 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1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/unit-3-loops-and-simulations/svg/1Unit 3: Loops and Simulations diagram 1Unit 3: Loops and Simulations - Intro to Python Fundamentals - diagram 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/unit-3-loops-and-simulations/svg/2Unit 3: Loops and Simulations diagram 2Unit 3: Loops and Simulations - Intro to Python Fundamentals - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#818cf8"/> </linearGradient> <pattern id="grid" width="30" height="30" patternUnits="userSpaceOnUse"> <path d="M 30 0 L 0 0 0 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Visual --> <path d="M 70 170 Q 100 160 130 180 T 190 170 T 250 190" fill="none" stroke="#ef4444" stroke-width="2" stroke-dasharray="4 2"/> <text x="70" y="210" font-family="system-ui, sans-serif" font-size="11" fill="#94a3b8">Linear "Spaghetti" Script</text> <!-- Modular Visual --> <rect x="70" y="240" width="40" height="25" rx="4" fill="#38bdf833" stroke="#38bdf8" stroke-width="1.5"/> <rect x="120" y="240" width="40" height="25" rx="4" fill="#38bdf833" stroke="#38bdf8" stroke-width="1.5"/> <rect x="170" y="240" width="40" height="25" rx="4" fill="#38bdf833" stroke="#38bdf8" stroke-width="1.5"/> <text x="70" y="285" font-family="system-ui, sans-serif" font-size="11" fill="#f8fafc">Modular Abstraction</text> <text x="70" y="300" font-family="system-ui, sans-serif" font-size="10" fill="#94a3b8">Interchangeable, reusable units.</text> <!-- Center Panel: The Function Machine --> <rect x="320" y="120" width="540" height="300" rx="16" fill="#ffffff05" stroke="#ffffff10"/> <text x="340" 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fill="#f8fafc">Numerical integration demonstrates modularity by encapsulating complex summation logic,</text> <text x="340" y="502" font-family="system-ui, sans-serif" font-size="12" fill="#f8fafc">allowing the user to treat a mathematical algorithm as a single "black box" tool.</text> <!-- Decorative Elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#ffffff10" stroke-width="8"/> <circle cx="850" cy="50" r="15" fill="#f59e0b" opacity="0.5"/> <!-- Marker Definition --> <defs> <marker id="arrow" markerWidth="10" markerHeight="10" refX="0" refY="3" orientation="auto" markerUnits="strokeWidth"> <path d="M0,0 L0,6 L9,3 z" fill="#f59e0b" /> </marker> </defs> </svg>Unit 4: Functions and Modularity image 1Unit 4: Functions and Modularity - Intro to Python Fundamentals - image 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/unit-4-functions-and-modularity/svg/1Unit 4: Functions and Modularity diagram 1Unit 4: Functions and Modularity - Intro to Python Fundamentals - diagram 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/unit-5-data-structures-lists/svg/1Unit 5: Data Structures - Lists and Sequences diagram 1Unit 5: Data Structures - Lists and Sequences - Intro to Python Fundamentals - diagram 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/unit-5-data-structures-lists/svg/2Unit 5: Data Structures - Lists and Sequences diagram 2Unit 5: Data Structures - Lists and Sequences - Intro to Python Fundamentals - diagram 2https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/unit-5-data-structures-lists/svg/3Unit 5: Data Structures - Lists and Sequences diagram 3Unit 5: Data Structures - Lists and Sequences - Intro to Python Fundamentals - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#334155" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Subtle Grid Lines --> <path d="M 0 100 L 900 100 M 0 460 L 900 460" stroke="#1e293b" stroke-width="1"/> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">UNIT 6: OBJECT-ORIENTED PROGRAMMING</text> <text x="40" y="85" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">A PARADIGM SHIFT FROM PROCEDURAL TO ENTITY-BASED DESIGN</text> <rect x="740" y="45" width="120" height="30" rx="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1"/> <text x="800" y="65" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8" text-anchor="middle">CORE CONCEPT</text> <!-- Left Card: Procedural vs OOP --> <rect x="40" y="120" width="260" height="160" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="150" font-family="sans-serif" font-size="18" font-weight="bold" fill="#e879f9">Procedural vs. OOP</text> <circle cx="70" cy="185" r="4" fill="#94a3b8"/> <text x="85" y="189" font-family="sans-serif" font-size="12" fill="#f8fafc">Procedural: The "How"</text> <text x="85" y="204" font-family="sans-serif" font-size="11" fill="#94a3b8">Linear sequence of actions.</text> <circle cx="70" cy="235" r="4" fill="#38bdf8"/> <text x="85" y="239" font-family="sans-serif" font-size="12" fill="#f8fafc">OOP: The "What"</text> <text x="85" y="254" font-family="sans-serif" font-size="11" fill="#94a3b8">Bundled data and logic (Objects).</text> <!-- Center Area: The Blueprint Illustration --> <rect x="320" y="120" width="540" height="240" rx="16" fill="#ffffff05" stroke="#ffffff10" stroke-dasharray="4 4"/> <!-- Blueprint Graphic --> <g transform="translate(360, 160)"> <!-- Blueprint Side --> <rect width="160" height="120" fill="#38bdf810" stroke="#38bdf8" stroke-width="1" stroke-dasharray="4 2"/> <path d="M 20 100 L 80 40 L 140 100 Z" fill="none" stroke="#38bdf8" stroke-width="2"/> <rect x="65" y="75" width="30" height="25" fill="none" stroke="#38bdf8" stroke-width="1"/> <text x="80" y="135" font-family="sans-serif" font-size="14" font-weight="bold" fill="#38bdf8" text-anchor="middle">CLASS (Blueprint)</text> <text x="80" y="150" font-family="sans-serif" font-size="10" fill="#94a3b8" text-anchor="middle">The Logical Template</text> <!-- Arrow --> <path d="M 180 60 L 240 60" stroke="#f59e0b" stroke-width="3" marker-end="url(#arrowhead)"/> <text x="210" y="50" font-family="sans-serif" font-size="10" font-weight="bold" fill="#f59e0b" text-anchor="middle">INSTANTIATE</text> <!-- Object Side --> <g transform="translate(260, 0)"> <rect width="160" height="120" rx="8" fill="#f59e0b20" stroke="#f59e0b" stroke-width="2"/> <path d="M 20 100 L 80 40 L 140 100 Z" fill="#f59e0b40" stroke="#f59e0b" stroke-width="2"/> <rect x="65" y="75" width="30" height="25" fill="#0f172a" stroke="#f59e0b" stroke-width="1"/> <text x="80" y="135" font-family="sans-serif" font-size="14" font-weight="bold" fill="#f59e0b" text-anchor="middle">OBJECT (Instance)</text> <text x="80" y="150" font-family="sans-serif" font-size="10" fill="#94a3b8" text-anchor="middle">Memory: 0x7ff...a2</text> </g> </g> <!-- Bottom Left: State Theorem --> <rect x="40" y="300" width="260" height="220" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="330" font-family="sans-serif" font-size="18" font-weight="bold" fill="#38bdf8">Object State</text> <text x="60" y="355" font-family="sans-serif" font-size="13" fill="#f8fafc" font-style="italic">σ(O, t) = { a₁:v₁, a₂:v₂ }</text> <text x="60" y="375" font-family="sans-serif" font-size="11" fill="#94a3b8" width="220"> The state of an object at time t is the </text> <text x="60" y="390" font-family="sans-serif" font-size="11" fill="#94a3b8"> mapping of all attributes to values. </text> <line x1="60" y1="410" x2="240" y2="410" stroke="#ffffff15" stroke-width="1"/> <text x="60" y="435" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">The 'self' Keyword</text> <text x="60" y="455" font-family="sans-serif" font-size="11" fill="#94a3b8">A reference to the specific instance</text> <text x="60" y="470" font-family="sans-serif" font-size="11" fill="#94a3b8">being accessed in memory.</text> <rect x="60" y="485" width="100" height="20" rx="4" fill="#38bdf820"/> <text x="110" y="500" font-family="monospace" font-size="11" fill="#38bdf8" text-anchor="middle">self.health = 100</text> <!-- 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Header Section --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="1">PRACTICAL PROGRAM DESIGN</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="16" font-weight="400" fill="#38bdf8" letter-spacing="2">THE ARCHITECTURE OF PROBLEM SOLVING</text> <rect x="400" y="95" width="100" height="3" fill="#f59e0b" rx="1.5"/> <!-- Left Column: The Pillars --> <g transform="translate(40, 130)"> <rect width="380" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="20" y="35" font-family="sans-serif" font-size="18" font-weight="700" fill="#e879f9">Core Pillars</text> <!-- Decomposition --> <g transform="translate(20, 55)"> <rect width="32" height="32" rx="6" fill="#e879f920" stroke="#e879f9" stroke-width="1.5"/> <path d="M10 10h4v4h-4zM18 10h4v4h-4zM10 18h4v4h-4zM18 18h4v4h-4z" fill="#e879f9"/> <text x="45" y="15" font-family="sans-serif" font-size="14" 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It requires managing a collection of objects, </text> <text x="100" y="70" font-family="sans-serif" font-size="13" fill="#94a3b8"> iterating through time steps, and handling state mutations based on conditional logic. </text> <!-- Code Snippet Visual --> <rect x="100" y="90" width="680" height="70" rx="8" fill="#00000040"/> <text x="120" y="115" font-family="monospace" font-size="12" fill="#38bdf8">while <tspan fill="#f8fafc">active:</tspan></text> <text x="140" y="135" font-family="monospace" font-size="12" fill="#94a3b8"># Sequence: Update State -> Render Output</text> <text x="140" y="150" font-family="monospace" font-size="12" fill="#e879f9">active = environment.run_cycle()</text> </g> </g> <!-- Decorative Connectors --> <path d="M230 310 L230 330" stroke="#ffffff15" stroke-width="2" fill="none"/> <path d="M650 310 L650 330" stroke="#ffffff15" stroke-width="2" fill="none"/> <!-- Footer Label --> <text x="860" y="540" text-anchor="end" font-family="sans-serif" font-size="10" font-weight="600" fill="#ffffff30" letter-spacing="1">CS CURRICULUM CAPSTONE // UNIT 08</text> </svg>Curriculum Wrap-up and Practical Design image 1Curriculum Wrap-up and Practical Design - Intro to Python Fundamentals - image 1https://www.getlykke.com/explore/public/intro-to-python-fundamentals-7d69e48a-d004-41fe-9114-c2d622302ba8/media/curriculum-wrap-up-and-projects/svg/1Curriculum Wrap-up and Practical Design diagram 1Curriculum Wrap-up and Practical Design - Intro to Python Fundamentals - diagram 1https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f2026-04-20T04:45:29.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="55" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">MARKET DYNAMICS</text> <text x="450" y="82" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="400" fill="#94a3b8" text-transform="uppercase" letter-spacing="3">Supply, Demand, and Equilibrium</text> <rect x="400" y="95" width="100" height="3" rx="1.5" fill="#f59e0b"/> <!-- Left Card: Demand --> <rect x="30" y="120" width="260" height="410" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="50" y="155" font-family="sans-serif" font-weight="700" font-size="20" 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fill="#cbd5e1">Marginal Cost of Production</text> <circle cx="635" cy="315" r="3" fill="#38bdf8"/> <text x="645" y="319" font-family="sans-serif" font-size="12" fill="#cbd5e1">Profit Maximization</text> <text x="630" y="360" font-family="sans-serif" font-weight="600" font-size="13" fill="#f8fafc">Shift Factors (Determinants):</text> <g transform="translate(630, 375)"> <rect width="220" height="110" rx="8" fill="#00000020"/> <text x="10" y="20" font-family="sans-serif" font-size="11" fill="#94a3b8">• Input Prices (Labor, Materials)</text> <text x="10" y="40" font-family="sans-serif" font-size="11" fill="#94a3b8">• Technological Advances</text> <text x="10" y="60" font-family="sans-serif" font-size="11" fill="#94a3b8">• Government Taxes/Subsidies</text> <text x="10" y="80" font-family="sans-serif" font-size="11" fill="#94a3b8">• Number of Sellers</text> <text x="10" y="100" font-family="sans-serif" font-size="11" fill="#94a3b8">• Producer Expectations</text> </g> <!-- Center: Equilibrium Visual --> <g transform="translate(310, 120)"> <rect width="280" height="410" rx="16" fill="#ffffff05"/> <!-- Graph --> <g transform="translate(40, 60)"> <!-- Axes --> <path d="M 0 0 L 0 200 L 200 200" fill="none" stroke="#94a3b8" stroke-width="2"/> <text x="-10" y="100" font-family="sans-serif" font-size="12" fill="#94a3b8" transform="rotate(-90 -10 100)" text-anchor="middle">Price (P)</text> <text x="100" y="220" font-family="sans-serif" font-size="12" fill="#94a3b8" text-anchor="middle">Quantity (Q)</text> <!-- Demand Curve --> <line x1="20" y1="20" x2="180" y2="180" stroke="#e879f9" stroke-width="4" stroke-linecap="round"/> <text x="185" y="185" font-family="sans-serif" font-weight="bold" font-size="14" fill="#e879f9">D</text> <!-- Supply Curve --> <line x1="20" y1="180" x2="180" y2="20" stroke="#38bdf8" stroke-width="4" stroke-linecap="round"/> <text x="185" y="25" font-family="sans-serif" font-weight="bold" font-size="14" fill="#38bdf8">S</text> <!-- Equilibrium Point --> <line 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font-family="sans-serif" font-size="11" fill="#f8fafc" font-style="italic">surplus or shortage."</text> </g> </g> <!-- Footer Info --> <text x="450" y="550" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#475569">ECONOMICS 101: VISUAL GUIDE TO MICROECONOMIC FOUNDATIONS</text> </svg>Supply, Demand, and Market Equilibrium image 1Supply, Demand, and Market Equilibrium - 14 01 Principles Of Microeconomics Fall 2018 - image 1https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f/media/supply-demand-equilibrium/svg/1Supply, Demand, and Market Equilibrium diagram 1Supply, Demand, and Market Equilibrium - 14 01 Principles Of Microeconomics Fall 2018 - diagram 1https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f/media/supply-demand-equilibrium/svg/2Supply, Demand, and Market Equilibrium diagram 2Supply, Demand, and Market Equilibrium - 14 01 Principles Of Microeconomics Fall 2018 - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="60" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="32" font-weight="bold" letter-spacing="1">MICROECONOMICS: THE DUALITY OF CHOICE</text> <rect x="350" y="75" width="200" height="4" fill="url(#accentGrad)" rx="2"/> <text x="450" y="100" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="300" text-transform="uppercase">The Study of Constrained Optimization</text> <!-- Central Bridge Logic --> <path d="M 450 140 L 450 480" stroke="#ffffff15" stroke-width="2" stroke-dasharray="8 4"/> <circle cx="450" cy="310" r="50" fill="#1e1b4b" stroke="#e879f9" stroke-width="2" filter="url(#glow)"/> <text x="450" y="305" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="24" font-style="italic">max</text> <text x="450" y="325" text-anchor="middle" fill="#e879f9" font-family="sans-serif" font-size="12" font-weight="bold">OPTIMUM</text> <!-- Left Panel: Consumer Theory --> <rect x="40" y="130" width="380" height="380" rx="16" fill="#ffffff08" stroke="#38bdf833" stroke-width="1"/> <rect 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Behavior</text> <text x="500" y="210" fill="#94a3b8" font-family="sans-serif" font-size="13">Goal: Maximize Economic Profit (π)</text> <!-- Firm Graph --> <g transform="translate(520, 240)"> <path d="M 0 0 L 0 120 L 150 120" fill="none" stroke="#94a3b8" stroke-width="2"/> <!-- Production Function --> <path d="M 0 120 Q 40 20 140 10" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <!-- Cost Line --> <line x1="20" y1="120" x2="140" y2="40" stroke="#e879f9" stroke-width="2" stroke-dasharray="4"/> <text x="160" y="125" fill="#94a3b8" font-family="sans-serif" font-size="10">Inputs (L, K)</text> <text x="-10" y="-10" fill="#94a3b8" font-family="sans-serif" font-size="10">Output (Q)</text> </g> <g transform="translate(500, 400)"> <rect width="340" height="90" rx="8" fill="#00000033"/> <text x="15" y="25" fill="#f8fafc" font-family="monospace" font-size="14">π = Total Revenue - Total Cost</text> <text x="15" y="50" fill="#94a3b8" font-family="sans-serif" font-size="12">Constraint: Q = f(Labor, Capital)</text> <text x="15" y="75" fill="#f59e0b" font-family="sans-serif" font-size="12" font-weight="bold">Condition: MR = MC</text> </g> <!-- Interaction Labels --> <g transform="translate(380, 525)"> <text x="70" y="0" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="11" font-style="italic">Rationality &amp; Consistency form the foundation of both actors.</text> </g> <!-- Decorative Accents --> <circle cx="40" cy="40" r="20" fill="#38bdf8" opacity="0.1"/> <circle cx="860" cy="520" r="30" fill="#e879f9" opacity="0.1"/> <path d="M 850 50 L 880 80" stroke="#f59e0b" stroke-width="2" opacity="0.3"/> <path d="M 860 40 L 890 70" stroke="#f59e0b" stroke-width="2" opacity="0.3"/> </svg>Consumer Theory and Firm Behavior image 1Consumer Theory and Firm Behavior - 14 01 Principles Of Microeconomics Fall 2018 - image 1https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f/media/consumer-and-producer-theory/svg/1Consumer Theory and Firm Behavior diagram 1Consumer Theory and Firm Behavior - 14 01 Principles Of Microeconomics Fall 2018 - diagram 1https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f/media/consumer-and-producer-theory/svg/2Consumer Theory and Firm Behavior diagram 2Consumer Theory and Firm Behavior - 14 01 Principles Of Microeconomics Fall 2018 - diagram 2https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f/media/market-structures/svg/1Market Structures and Competition diagram 1Market Structures and Competition - 14 01 Principles Of Microeconomics Fall 2018 - diagram 1https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f/media/market-structures/svg/2Market Structures and Competition diagram 2Market Structures and Competition - 14 01 Principles Of Microeconomics Fall 2018 - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="40" y="60" font-family="Inter, system-ui, sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-0.02em">WELFARE ECONOMICS &amp; PUBLIC POLICY</text> <text x="40" y="85" font-family="Inter, system-ui, sans-serif" font-size="14" fill="#94a3b8" font-weight="500">The Normative Framework for Social Well-being and Market Intervention</text> <rect x="40" y="105" width="820" height="2" fill="#38bdf8" fill-opacity="0.3"/> <!-- Left Column: The Theoretical Ideal --> <rect x="40" y="130" width="390" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="65" y="160" font-family="Inter, system-ui, sans-serif" font-weight="700" font-size="18" fill="#38bdf8">The Theoretical Ideal</text> <!-- Icon: Efficiency --> <circle cx="80" cy="210" r="25" fill="none" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2"/> <circle cx="80" cy="210" r="12" fill="#38bdf8" fill-opacity="0.4"/> <text x="120" y="195" font-family="Inter, sans-serif" font-weight="600" font-size="14" fill="#f8fafc">Pareto Efficiency</text> <text x="120" y="212" font-family="Inter, sans-serif" font-size="12" fill="#94a3b8">No one can be made better off without</text> <text x="120" y="227" font-family="Inter, sans-serif" font-size="12" fill="#94a3b8">making someone else worse off.</text> <text x="65" y="265" font-family="Inter, sans-serif" font-weight="600" font-size="13" fill="#f1f5f9">1st Theorem:</text> <text x="155" y="265" font-family="Inter, sans-serif" font-size="13" fill="#94a3b8">Markets lead to efficiency.</text> <text x="65" y="285" font-family="Inter, sans-serif" font-weight="600" font-size="13" fill="#f1f5f9">2nd Theorem:</text> <text x="155" y="285" font-family="Inter, sans-serif" font-size="13" fill="#94a3b8">Any efficient outcome is reachable.</text> <!-- Right Column: Market Failures --> <rect x="470" y="130" width="390" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="495" y="160" font-family="Inter, system-ui, sans-serif" font-weight="700" font-size="18" fill="#f59e0b">The Reality: Market Failures</text> <!-- Failure Grid --> <g transform="translate(495, 185)"> <!-- Externalities --> <rect width="170" height="40" rx="8" fill="#f59e0b15"/> <text x="10" y="25" font-family="Inter, sans-serif" font-weight="600" font-size="12" fill="#fef3c7">Externalities</text> <circle cx="150" cy="20" r="5" fill="#f59e0b"/> <!-- Public Goods --> <rect y="50" width="170" height="40" rx="8" fill="#f59e0b15"/> <text x="10" y="75" font-family="Inter, sans-serif" font-weight="600" font-size="12" fill="#fef3c7">Public Goods</text> <path d="M145 70 l10 10 m0 -10 l-10 10" stroke="#f59e0b" stroke-width="2"/> <!-- Asymmetric Info --> <rect x="185" width="170" height="40" rx="8" fill="#f59e0b15"/> <text x="195" y="25" font-family="Inter, sans-serif" font-weight="600" font-size="12" fill="#fef3c7">Asymmetric Info</text> <rect x="330" y="15" width="10" height="10" fill="none" stroke="#f59e0b" stroke-width="2"/> <!-- Market Power --> <rect x="185" y="50" width="170" height="40" rx="8" fill="#f59e0b15"/> <text x="195" y="75" font-family="Inter, sans-serif" font-weight="600" font-size="12" fill="#fef3c7">Market Power</text> <path d="M330 70 h10 v10 h-10 z" fill="#f59e0b"/> </g> <text x="495" y="295" font-family="Inter, sans-serif" font-size="12" fill="#94a3b8">Condition: MSB ≠ MSC (Inefficient Allocation)</text> <!-- Bottom Section: Policy Tools --> <rect x="40" y="330" width="820" height="200" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="65" y="365" font-family="Inter, system-ui, sans-serif" font-weight="700" font-size="18" fill="#e879f9">Policy Interventions</text> <!-- Tool 1: Pigouvian Tax --> <g transform="translate(65, 390)"> <rect width="240" height="115" rx="12" fill="#e879f908" stroke="#e879f930"/> <text x="15" y="25" font-family="Inter, sans-serif" font-weight="700" font-size="14" fill="#fdf4ff">Pigouvian Taxes</text> <text x="15" y="45" font-family="Inter, sans-serif" font-size="11" fill="#94a3b8">Internalizing Externalities</text> <!-- Mini Graph --> <line x1="20" y1="100" x2="80" y2="100" stroke="#94a3b8" stroke-width="1"/> <line x1="20" y1="100" x2="20" y2="60" stroke="#94a3b8" stroke-width="1"/> <path d="M20 90 Q 50 85 80 65" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="100" y="75" font-family="serif" font-style="italic" font-size="12" fill="#e879f9">t = MEC</text> <text x="100" y="95" font-family="Inter, sans-serif" font-size="11" fill="#94a3b8">Aligns MPC with MSC</text> </g> <!-- Tool 2: Public Provision --> <g transform="translate(330, 390)"> <rect width="240" height="115" rx="12" fill="#e879f908" stroke="#e879f930"/> <text x="15" y="25" font-family="Inter, sans-serif" font-weight="700" font-size="14" fill="#fdf4ff">Public Provision</text> <text x="15" y="45" font-family="Inter, sans-serif" font-size="11" fill="#94a3b8">Solving the Free-Rider Problem</text> <circle cx="40" cy="85" r="15" fill="#e879f9" fill-opacity="0.2" stroke="#e879f9" stroke-width="1"/> <circle cx="55" cy="85" r="15" fill="#e879f9" fill-opacity="0.2" stroke="#e879f9" stroke-width="1"/> <text x="85" y="80" font-family="Inter, sans-serif" font-size="11" fill="#f8fafc">Samuelson Condition:</text> <text x="85" y="95" font-family="serif" font-style="italic" font-size="12" fill="#e879f9">Σ MB = MC</text> </g> <!-- Tool 3: Regulation --> <g transform="translate(595, 390)"> <rect width="240" height="115" rx="12" fill="#e879f908" stroke="#e879f930"/> <text x="15" y="25" font-family="Inter, sans-serif" font-weight="700" font-size="14" fill="#fdf4ff">Regulation &amp; Law</text> <text x="15" y="45" font-family="Inter, sans-serif" font-size="11" fill="#94a3b8">Correcting Information &amp; Power</text> <rect x="20" y="65" width="40" height="30" rx="4" fill="none" stroke="#e879f9" stroke-width="1.5"/> <line x1="25" y1="75" x2="55" y2="75" stroke="#e879f9" stroke-width="1"/> <line x1="25" y1="85" x2="45" y2="85" stroke="#e879f9" stroke-width="1"/> <text x="75" y="75" font-family="Inter, sans-serif" font-size="11" fill="#94a3b8">• Antitrust Laws</text> <text x="75" y="90" font-family="Inter, sans-serif" font-size="11" fill="#94a3b8">• Disclosure Mandates</text> <text x="75" y="105" font-family="Inter, sans-serif" font-size="11" fill="#94a3b8">• Property Rights (Coase)</text> </g> <!-- Decorative Accents --> <circle cx="850" cy="50" r="30" fill="#38bdf8" fill-opacity="0.05"/> <circle cx="850" cy="50" r="15" fill="#38bdf8" fill-opacity="0.1"/> <path d="M830 510 L870 510 M850 490 L850 530" stroke="#ffffff10" stroke-width="2"/> </svg>Welfare Economics and Public Policy image 1Welfare Economics and Public Policy - 14 01 Principles Of Microeconomics Fall 2018 - image 1https://www.getlykke.com/explore/public/14-01-principles-of-microeconomics-fall-c9db27b0-c48b-44cd-b5ce-76fe7a34729f/media/welfare-economics-public-policy/svg/1Welfare Economics and Public Policy diagram 1Welfare Economics and Public Policy - 14 01 Principles Of Microeconomics Fall 2018 - diagram 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b62026-04-20T04:43:10.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="32" font-weight="bold" letter-spacing="1">FOUNDATIONS OF CHEMISTRY</text> <text x="450" y="78" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="16" font-weight="300" letter-spacing="2">MATTER • MEASUREMENT • ATOMIC THEORY</text> <line x1="300" y1="95" x2="600" y2="95" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 4"/> <!-- Left Panel: Atomic Theory --> <rect x="30" y="120" width="410" height="280" rx="16" fill="#ffffff10" stroke="#ffffff20"/> <text x="50" y="150" fill="#e879f9" font-family="sans-serif" font-size="18" font-weight="bold">I. ATOMIC THEORY</text> <text x="50" y="170" fill="#94a3b8" font-family="sans-serif" font-size="12">The "Source Code" of Matter</text> <!-- Atom Illustration --> <circle cx="100" cy="240" r="15" fill="#e879f933" stroke="#e879f9" stroke-width="2"/> <circle cx="96" cy="236" r="4" fill="#38bdf8"/> <circle cx="104" cy="244" r="4" fill="#f59e0b"/> <ellipse cx="100" cy="240" rx="40" ry="15" fill="none" stroke="#ffffff30" stroke-width="1" transform="rotate(45 100 240)"/> <ellipse cx="100" cy="240" rx="40" ry="15" fill="none" stroke="#ffffff30" stroke-width="1" transform="rotate(-45 100 240)"/> <circle cx="128" cy="212" r="3" fill="#f8fafc" filter="url(#glow)"/> <!-- Subatomic Table --> <g transform="translate(160, 200)"> <rect width="250" height="80" rx="8" fill="#00000030"/> <text x="10" y="20" fill="#f8fafc" font-family="sans-serif" font-size="11" font-weight="bold">Particle</text> <text x="80" y="20" fill="#f8fafc" font-family="sans-serif" font-size="11" font-weight="bold">Charge</text> <text x="150" y="20" fill="#f8fafc" font-family="sans-serif" font-size="11" font-weight="bold">Mass (amu)</text> <text x="10" y="40" fill="#38bdf8" font-family="sans-serif" font-size="11">Proton (p+)</text> <text x="80" y="40" fill="#94a3b8" font-family="sans-serif" font-size="11">+1</text> <text x="150" y="40" fill="#94a3b8" font-family="sans-serif" font-size="11">1.0073</text> <text x="10" y="55" fill="#f59e0b" font-family="sans-serif" font-size="11">Neutron (n0)</text> <text x="80" y="55" fill="#94a3b8" font-family="sans-serif" font-size="11">0</text> <text x="150" y="55" fill="#94a3b8" font-family="sans-serif" font-size="11">1.0087</text> <text x="10" y="70" fill="#e879f9" font-family="sans-serif" font-size="11">Electron (e-)</text> <text x="80" y="70" fill="#94a3b8" font-family="sans-serif" font-size="11">-1</text> <text x="150" y="70" fill="#94a3b8" font-family="sans-serif" font-size="11">0.0005</text> </g> <text x="50" y="320" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="bold">Isotopes &amp; Atomic Mass</text> <text x="50" y="340" fill="#94a3b8" font-family="sans-serif" font-size="12" width="350"> Atomic Number (Z) defines identity. Mass Number (A) </text> <text x="50" y="355" fill="#94a3b8" font-family="sans-serif" font-size="12"> varies by neutron count. Atomic mass is a weighted average. </text> <!-- Right Panel: Measurement --> <rect x="460" y="120" width="410" height="280" rx="16" fill="#ffffff10" stroke="#ffffff20"/> <text x="480" y="150" fill="#38bdf8" font-family="sans-serif" font-size="18" font-weight="bold">II. MEASUREMENT &amp; SI</text> <text x="480" y="170" fill="#94a3b8" font-family="sans-serif" font-size="12">The Language of Precision</text> <!-- SI Units List --> <g transform="translate(480, 190)"> <text x="0" y="15" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">SI BASE UNITS</text> <rect x="0" y="25" width="180" height="100" rx="8" fill="#00000030"/> <text x="10" y="45" fill="#38bdf8" font-family="sans-serif" font-size="11">Mass: Kilogram (kg)</text> <text x="10" y="60" fill="#38bdf8" font-family="sans-serif" font-size="11">Length: Meter (m)</text> <text x="10" y="75" fill="#38bdf8" font-family="sans-serif" font-size="11">Temp: Kelvin (K)</text> <text x="10" y="90" fill="#38bdf8" font-family="sans-serif" font-size="11">Amount: Mole (mol)</text> <text x="10" y="105" fill="#38bdf8" font-family="sans-serif" font-size="11">Time: Second (s)</text> </g> <!-- Accuracy vs Precision Graphic --> <g transform="translate(680, 190)"> <text x="0" y="15" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">PRECISION VS ACCURACY</text> <!-- Target 1 --> <circle cx="30" cy="60" r="25" fill="none" stroke="#ffffff20" stroke-width="1"/> <circle cx="30" cy="60" r="15" fill="none" stroke="#ffffff20" stroke-width="1"/> <circle cx="30" cy="60" r="5" fill="#f59e0b33"/> <circle cx="45" cy="45" r="2" fill="#f59e0b"/> <circle cx="47" cy="48" r="2" fill="#f59e0b"/> <circle cx="43" cy="50" r="2" fill="#f59e0b"/> <text x="30" y="100" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="10">Precise, Not Accurate</text> <!-- Target 2 --> <circle cx="120" cy="60" r="25" fill="none" stroke="#ffffff20" stroke-width="1"/> <circle cx="120" cy="60" r="15" fill="none" stroke="#ffffff20" stroke-width="1"/> <circle cx="120" cy="60" r="5" fill="#38bdf833"/> <circle cx="120" cy="60" r="2" fill="#38bdf8"/> <circle cx="122" cy="58" r="2" fill="#38bdf8"/> <circle cx="118" cy="62" r="2" fill="#38bdf8"/> <text x="120" y="100" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="10">Precise &amp; Accurate</text> </g> <!-- Bottom Panel: Dimensional Analysis --> <rect x="30" y="420" width="840" height="110" rx="16" fill="#ffffff15" stroke="#38bdf840"/> <text x="50" y="450" fill="#f59e0b" font-family="sans-serif" font-size="18" font-weight="bold">III. DIMENSIONAL ANALYSIS</text> <text x="50" y="470" fill="#94a3b8" font-family="sans-serif" font-size="12">The Factor-Label Method: Treating units as algebraic quantities.</text> <!-- Equation Visual --> <g transform="translate(50, 485)"> <rect width="120" height="30" rx="4" fill="#ffffff10"/> <text x="60" y="20" text-anchor="middle" fill="#f8fafc" font-family="monospace" font-size="14">Given Unit</text> <text x="140" y="20" fill="#f8fafc" font-size="18">×</text> <line x1="165" y1="20" x2="285" y2="20" stroke="#f8fafc" stroke-width="1"/> <text x="225" y="15" text-anchor="middle" fill="#38bdf8" font-family="monospace" font-size="12">Desired Unit</text> <text x="225" y="35" text-anchor="middle" fill="#e879f9" font-family="monospace" font-size="12">Given Unit</text> <text x="305" y="20" fill="#f8fafc" font-size="18">=</text> <rect x="330" y="0" width="120" height="30" rx="4" fill="#38bdf830" stroke="#38bdf8"/> <text x="390" y="20" text-anchor="middle" fill="#f8fafc" font-family="monospace" font-size="14" font-weight="bold">Desired Unit</text> <text x="480" y="20" fill="#94a3b8" font-family="sans-serif" font-size="11" font-style="italic">"Units must cancel out to ensure physical logic."</text> </g> <!-- Decorative elements --> <path d="M 850 50 L 870 70 M 870 50 L 850 70" stroke="#f59e0b" stroke-width="2" opacity="0.5"/> <circle cx="40" cy="40" r="10" fill="none" stroke="#38bdf8" stroke-width="2" opacity="0.5"/> </svg>Foundations of Chemistry: Matter and Measurement image 1Foundations of Chemistry: Matter and Measurement - Chemistry 2e - image 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/foundations-of-chemistry/svg/1Foundations of Chemistry: Matter and Measurement diagram 1Foundations of Chemistry: Matter and Measurement - Chemistry 2e - diagram 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/foundations-of-chemistry/svg/2Foundations of Chemistry: Matter and Measurement diagram 2Foundations of Chemistry: Matter and Measurement - Chemistry 2e - diagram 2https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/electronic-structure-and-bonding/svg/1Electronic Structure and Chemical Bonding diagram 1Electronic Structure and Chemical Bonding - Chemistry 2e - diagram 1<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff08" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" filter="url(#glow)">STATES OF MATTER &amp; 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London Dispersion</text> <text x="350" y="125" text-anchor="end" font-family="sans-serif" font-size="11" fill="#94a3b8">All Matter (Weakest)</text> </g> <!-- Bottom Panel: Real Gases & Thermochemistry --> <rect x="40" y="370" width="820" height="160" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="400" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">Real Gas Deviations: Van der Waals</text> <text x="60" y="430" font-family="sans-serif" font-size="13" fill="#f8fafc" font-style="italic">[P + a(n/V)²][V - nb] = nRT</text> <g transform="translate(60, 450)"> <rect width="340" height="60" rx="8" fill="#f59e0b10" stroke="#f59e0b30"/> <text x="15" y="25" font-family="sans-serif" font-weight="700" font-size="14" fill="#f59e0b">Constant 'a'</text> <text x="15" y="45" font-family="sans-serif" font-size="11" fill="#94a3b8">Corrects for intermolecular attraction forces.</text> </g> <g transform="translate(420, 450)"> <rect width="340" height="60" rx="8" fill="#f59e0b10" stroke="#f59e0b30"/> <text x="15" y="25" font-family="sans-serif" font-weight="700" font-size="14" fill="#f59e0b">Constant 'b'</text> <text x="15" y="45" font-family="sans-serif" font-size="11" fill="#94a3b8">Corrects for the finite volume of particles.</text> </g> <!-- Decorative Energy Flow --> <path d="M 450 350 L 450 370" stroke="url(#accentGrad)" stroke-width="2" stroke-dasharray="4 4"/> <circle cx="450" cy="360" r="4" fill="#f59e0b"/> <!-- Visualizing Particles (Small Iconography) --> <g transform="translate(350, 125)"> <circle cx="10" cy="10" r="4" fill="#38bdf8"/> <line x1="14" y1="14" x2="22" y2="22" stroke="#38bdf8" stroke-width="1"/> <circle cx="30" cy="5" r="4" fill="#38bdf8"/> <line x1="30" y1="9" x2="30" y2="18" stroke="#38bdf8" stroke-width="1"/> <circle cx="5" cy="35" r="4" fill="#38bdf8"/> <line x1="9" y1="35" x2="18" y2="35" stroke="#38bdf8" stroke-width="1"/> </g> <g transform="translate(780, 125)"> <circle cx="10" cy="10" r="4" fill="#e879f9"/> <circle cx="18" cy="10" r="4" fill="#e879f9"/> <circle cx="14" cy="17" r="4" fill="#e879f9"/> <path d="M 10 10 Q 14 10 18 10" stroke="#ffffff40" fill="none" stroke-width="1"/> </g> <!-- Footer Label --> <text x="860" y="545" text-anchor="end" font-family="sans-serif" font-size="10" font-weight="bold" fill="#ffffff20">THERMODYNAMICS SERIES // VOL 01</text> </svg>States of Matter and Thermochemistry image 1States of Matter and Thermochemistry - Chemistry 2e - image 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/states-of-matter-and-thermochemistry/svg/1States of Matter and Thermochemistry diagram 1States of Matter and Thermochemistry - Chemistry 2e - diagram 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/states-of-matter-and-thermochemistry/svg/2States of Matter and Thermochemistry diagram 2States of Matter and Thermochemistry - Chemistry 2e - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg-grad" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dot-pattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <linearGradient id="kinetics-grad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#818cf8"/> </linearGradient> <linearGradient id="equil-grad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#f59e0b"/> <stop offset="100%" stop-color="#fb7185"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg-grad)"/> <rect width="900" height="560" fill="url(#dot-pattern)"/> <!-- Subtle Grid Lines --> <g stroke="#ffffff08" stroke-width="1"> <line x1="450" y1="100" x2="450" y2="520"/> <line x1="50" y1="280" x2="850" y2="280"/> </g> <!-- Header --> <text x="450" y="55" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">CHEMICAL KINETICS &amp; EQUILIBRIUM</text> <text x="450" y="80" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="2">THE DYNAMICS OF CHEMICAL REACTIVITY</text> <!-- LEFT PANEL: KINETICS --> <rect x="40" y="110" width="400" height="410" rx="20" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="65" y="145" font-family="sans-serif" font-weight="700" font-size="20" fill="#38bdf8">KINETICS: THE CLOCK</text> <text x="65" y="165" font-family="sans-serif" font-size="12" fill="#94a3b8">Focus: Reaction Rates &amp; Mechanisms (How Fast?)</text> <!-- Energy Profile Diagram --> <g transform="translate(70, 190)"> <path d="M 0,120 Q 50,120 80,120 T 150,20 T 220,100 L 340,100" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <line x1="0" y1="130" x2="0" y2="0" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4"/> <line x1="0" y1="130" x2="340" y2="130" stroke="#94a3b8" stroke-width="1" stroke-dasharray="4"/> <!-- Activation Energy Label --> <path d="M 150,120 L 150,25" stroke="#f472b6" stroke-width="2" marker-start="url(#arrow)" marker-end="url(#arrow)"/> <text x="155" y="70" font-family="sans-serif" font-size="11" fill="#f472b6" font-weight="bold">Eₐ (Activation Energy)</text> <!-- Transition State --> <circle cx="150" cy="20" r="4" fill="#f8fafc"/> <text x="120" y="12" font-family="sans-serif" font-size="10" fill="#f8fafc">Transition State</text> <text x="5" y="115" font-family="sans-serif" font-size="10" fill="#94a3b8">Reactants</text> <text x="280" y="95" font-family="sans-serif" font-size="10" fill="#94a3b8">Products</text> </g> <!-- Kinetics Details --> <g transform="translate(65, 360)"> <rect width="350" height="140" rx="12" fill="#00000020"/> <text x="15" y="25" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">Collision Theory</text> <text x="15" y="45" font-family="sans-serif" font-size="11" fill="#94a3b8">1. Molecules must collide</text> <text x="15" y="60" font-family="sans-serif" font-size="11" fill="#94a3b8">2. Correct orientation required</text> <text x="15" y="75" font-family="sans-serif" font-size="11" fill="#94a3b8">3. Sufficient kinetic energy (Eₐ)</text> <text x="190" y="25" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">Rate Law</text> <text x="190" y="50" font-family="sans-serif" font-size="16" fill="#38bdf8" font-style="italic">Rate = k[A]ᵐ[B]ⁿ</text> <text x="190" y="75" font-family="sans-serif" font-size="11" fill="#94a3b8">k = Arrhenius Constant</text> </g> <!-- RIGHT PANEL: EQUILIBRIUM --> <rect x="460" y="110" width="400" height="410" rx="20" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="485" y="145" font-family="sans-serif" font-weight="700" font-size="20" fill="#f59e0b">EQUILIBRIUM: THE BALANCE</text> <text x="485" y="165" font-family="sans-serif" font-size="12" fill="#94a3b8">Focus: Reversibility &amp; Final State (Where?)</text> <!-- Balance Scale Icon --> <g transform="translate(660, 220)"> <path d="M -80,40 L 80,40" stroke="#f59e0b" stroke-width="4" stroke-linecap="round"/> <path d="M 0,40 L 0,-20" stroke="#94a3b8" stroke-width="2"/> <circle cx="-80" cy="60" r="20" fill="none" stroke="#f59e0b" stroke-width="2"/> <circle cx="80" cy="60" r="20" fill="none" stroke="#f59e0b" stroke-width="2"/> <text x="-80" y="65" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f8fafc" font-weight="bold">R</text> <text x="80" y="65" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f8fafc" font-weight="bold">P</text> <path d="M -20,10 L 20,10 M 20,0 L 30,10 L 20,20 M -20,0 L -30,10 L -20,20" fill="none" stroke="#f8fafc" stroke-width="2"/> <text x="0" y="-30" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#f59e0b" font-weight="bold">Rate_f = Rate_r</text> </g> <!-- Equilibrium Graph --> <g transform="translate(485, 280)"> <line x1="0" y1="60" x2="160" y2="60" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2"/> <!-- Reactant curve --> <path d="M 0,10 Q 40,80 160,80" fill="none" stroke="#fb7185" stroke-width="2"/> <!-- Product curve --> <path d="M 0,100 Q 40,40 160,40" fill="none" stroke="#34d399" stroke-width="2"/> <text x="165" y="85" font-family="sans-serif" font-size="10" fill="#fb7185">[Reactants]</text> <text x="165" y="45" font-family="sans-serif" font-size="10" fill="#34d399">[Products]</text> <text x="80" y="115" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">Time →</text> <line x1="60" y1="0" x2="60" y2="100" stroke="#f8fafc30" stroke-width="1"/> <text x="65" y="10" font-family="sans-serif" font-size="9" fill="#f8fafc60">Equilibrium Reached</text> </g> <!-- Equilibrium Details --> <g transform="translate(485, 410)"> <rect width="350" height="90" rx="12" fill="#00000020"/> <text x="15" y="25" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">Le Chatelier's Principle</text> <text x="15" y="45" font-family="sans-serif" font-size="11" fill="#94a3b8">A system at equilibrium responds to</text> <text x="15" y="60" font-family="sans-serif" font-size="11" fill="#94a3b8">stress (T, P, Conc) by shifting to</text> <text x="15" y="75" font-family="sans-serif" font-size="11" fill="#94a3b8">counteract the change.</text> <text x="210" y="25" font-family="sans-serif" font-weight="700" font-size="13" fill="#f8fafc">Constant (K)</text> <text x="210" y="55" font-family="sans-serif" font-size="16" fill="#f59e0b" font-weight="bold">K = [Prod] / [React]</text> </g> <!-- Central Connector --> <g transform="translate(430, 260)"> <rect x="-20" y="-20" width="80" height="40" rx="10" fill="#1e1b4b" stroke="#f472b6" stroke-width="2"/> <text x="20" y="5" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f8fafc">VS</text> </g> <!-- Bottom Legend/Key Facts --> <rect x="40" y="530" width="820" height="20" rx="4" fill="#ffffff05"/> <text x="450" y="544" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#64748b" text-transform="uppercase" letter-spacing="1">Thermodynamics determines IF • Kinetics determines WHEN • Equilibrium determines HOW MUCH</text> </svg>Chemical Kinetics and Equilibrium image 1Chemical Kinetics and Equilibrium - Chemistry 2e - image 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/kinetics-and-equilibrium/svg/1Chemical Kinetics and Equilibrium diagram 1Chemical Kinetics and Equilibrium - Chemistry 2e - diagram 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/kinetics-and-equilibrium/svg/2Chemical Kinetics and Equilibrium diagram 2Chemical Kinetics and Equilibrium - Chemistry 2e - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Decorative Elements --> <circle cx="850" cy="50" r="100" fill="#38bdf8" fill-opacity="0.05"/> <circle cx="50" cy="510" r="80" fill="#e879f9" fill-opacity="0.05"/> <!-- Header --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">THERMODYNAMICS &amp; ELECTROCHEMISTRY</text> <text x="40" y="85" font-family="sans-serif" font-size="16" fill="#94a3b8" letter-spacing="1">THE ROADMAP OF CHEMICAL SPONTANEITY</text> <line x1="40" y1="105" x2="860" y2="105" stroke="#38bdf8" stroke-width="2" stroke-opacity="0.3"/> <!-- Left Card: Entropy --> <rect x="40" y="130" width="400" height="200" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <text x="65" y="165" font-family="sans-serif" font-weight="700" font-size="20" fill="#38bdf8">ENTROPY (S)</text> <text x="65" y="185" font-family="sans-serif" font-size="13" fill="#94a3b8">The measure of energy dispersal &amp; microstates.</text> <!-- Boltzmann Equation Graphic --> <rect x="65" y="205" width="180" height="60" rx="8" fill="#00000030"/> <text x="85" y="242" font-family="serif" font-style="italic" font-size="24" fill="#f8fafc">S = k<tspan baseline-shift="sub" font-size="14">B</tspan> ln W</text> <!-- Microstate Visual --> <g transform="translate(270, 205)"> <rect width="140" height="90" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <circle cx="20" cy="20" r="4" fill="#f59e0b"/> <circle cx="50" cy="35" r="4" fill="#f59e0b"/> <circle cx="30" cy="60" r="4" fill="#f59e0b"/> <circle cx="80" cy="25" r="4" fill="#f59e0b"/> <circle cx="110" cy="50" r="4" fill="#f59e0b"/> <circle cx="70" cy="70" r="4" fill="#f59e0b"/> <text x="70" y="105" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#94a3b8">Energy Dispersal (W)</text> </g> <!-- Right Card: Gibbs Free Energy --> <rect x="460" y="130" width="400" height="200" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <text x="485" y="165" font-family="sans-serif" font-weight="700" font-size="20" fill="#e879f9">GIBBS FREE ENERGY (G)</text> <text x="485" y="185" font-family="sans-serif" font-size="13" fill="#94a3b8">The energy available to perform useful work.</text> <!-- Gibbs Equation Graphic --> <rect x="485" y="205" width="220" height="60" rx="8" fill="#00000030"/> <text x="505" y="242" font-family="serif" font-style="italic" font-size="24" fill="#f8fafc">ΔG = ΔH - TΔS</text> <!-- Spontaneity Icon --> <g transform="translate(730, 205)"> <circle cx="50" cy="45" r="35" fill="none" stroke="#e879f9" stroke-width="2" stroke-dasharray="4 2"/> <path d="M 50 20 L 50 70 M 35 55 L 50 70 L 65 55" fill="none" stroke="#f8fafc" stroke-width="3"/> <text x="50" y="105" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#94a3b8">Spontaneous if ΔG &lt; 0</text> </g> <!-- Bottom Section: Spontaneity Matrix --> <rect x="40" y="350" width="820" height="180" rx="16" fill="#ffffff08" stroke="#ffffff10"/> <text x="65" y="380" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">THE SPONTANEITY MATRIX</text> <!-- Matrix Grid --> <g transform="translate(65, 400)"> <!-- Headers --> <text x="150" y="0" font-family="sans-serif" font-size="12" fill="#94a3b8" text-anchor="middle">+ ΔS (Dispersal)</text> <text x="350" y="0" font-family="sans-serif" font-size="12" fill="#94a3b8" text-anchor="middle">- ΔS (Order)</text> <text x="-10" y="45" font-family="sans-serif" font-size="12" fill="#94a3b8" text-anchor="end" transform="rotate(-90, -10, 45)">- ΔH (Exo)</text> <text x="-10" y="115" font-family="sans-serif" font-size="12" fill="#94a3b8" text-anchor="end" transform="rotate(-90, -10, 115)">+ ΔH (Endo)</text> <!-- Cells --> <rect x="50" y="15" width="200" height="45" rx="6" fill="#10b98120" stroke="#10b98140"/> <text x="150" y="43" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#10b981">Always Spontaneous</text> <rect x="255" y="15" width="200" height="45" rx="6" fill="#38bdf820" stroke="#38bdf840"/> <text x="355" y="43" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">Spontaneous at LOW T</text> <rect x="50" y="65" width="200" height="45" rx="6" fill="#f59e0b20" stroke="#f59e0b40"/> <text x="150" y="93" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f59e0b">Spontaneous at HIGH T</text> <rect x="255" y="65" width="200" height="45" rx="6" fill="#ef444420" stroke="#ef444440"/> <text x="355" y="93" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#ef4444">Never Spontaneous</text> <!-- Electrochemistry Bridge --> <g transform="translate(500, 0)"> <rect width="270" height="110" rx="12" fill="#ffffff05" stroke="#38bdf830"/> <text x="135" y="25" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="14" fill="#38bdf8">ELECTROCHEMICAL BRIDGE</text> <text x="135" y="55" text-anchor="middle" font-family="serif" font-style="italic" font-size="20" fill="#f8fafc">ΔG° = -nFE°<tspan baseline-shift="sub" font-size="12">cell</tspan></text> <text x="135" y="85" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#94a3b8">Linking Potential (E) to Free Energy (G)</text> <path d="M 20 95 L 250 95" stroke="#38bdf8" stroke-width="1" stroke-dasharray="2 2"/> </g> </g> <!-- Footer Accents --> <rect x="40" y="545" width="820" height="4" rx="2" fill="#38bdf8" fill-opacity="0.2"/> <circle cx="450" cy="547" r="6" fill="#38bdf8"/> </svg>Thermodynamics and Electrochemistry image 1Thermodynamics and Electrochemistry - Chemistry 2e - image 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/thermodynamics-and-electrochemistry/svg/1Thermodynamics and Electrochemistry diagram 1Thermodynamics and Electrochemistry - Chemistry 2e - diagram 1https://www.getlykke.com/explore/public/chemistry-2e-61aaa542-40da-45df-8ae5-3e14c99880b6/media/thermodynamics-and-electrochemistry/svg/2Thermodynamics and Electrochemistry diagram 2Thermodynamics and Electrochemistry - Chemistry 2e - diagram 2https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e02026-04-20T04:40:11.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dotPattern" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#334155" fill-opacity="0.5"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dotPattern)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="1">SAMPLING &amp; DATA</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="400" fill="#94a3b8" text-transform="uppercase" letter-spacing="3">The Architecture of Statistical Inquiry</text> <rect x="400" y="85" width="100" height="3" fill="#f59e0b" rx="1.5"/> <!-- Main Panels --> <!-- Panel 1: Population vs Sample --> <rect x="30" y="110" width="270" height="340" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="165" y="140" text-anchor="middle" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">I. The Duality</text> <!-- Population Circle --> <circle cx="165" cy="210" r="50" fill="#38bdf815" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2"/> <g fill="#38bdf8" opacity="0.6"> <circle cx="145" cy="195" r="3"/><circle cx="180" cy="200" r="3"/><circle cx="160" cy="225" r="3"/> <circle cx="190" cy="220" r="3"/><circle cx="140" cy="215" r="3"/><circle cx="165" cy="185" r="3"/> </g> <text x="165" y="275" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">POPULATION (N)</text> <text x="165" y="292" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#94a3b8">The entire "Universe"</text> <!-- Sample Selection Arrow --> <path d="M165 310 L165 340" stroke="#f59e0b" stroke-width="2" marker-end="url(#arrowhead)"/> <!-- Sample Circle --> <circle cx="165" cy="380" r="30" fill="#f59e0b15" stroke="#f59e0b" stroke-width="2"/> <g fill="#f59e0b"> <circle cx="160" cy="375" r="3"/><circle cx="175" cy="385" r="3"/><circle cx="155" cy="390" r="3"/> </g> <text x="165" y="425" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">SAMPLE (n)</text> <text x="165" y="440" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#94a3b8">The Tangible Subset</text> <!-- Panel 2: Parameters vs Statistics --> <rect x="315" y="110" width="270" height="340" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="450" y="140" text-anchor="middle" font-family="sans-serif" font-size="18" font-weight="700" fill="#e879f9">II. Metrics</text> <!-- Table Structure --> <rect x="335" y="160" width="230" height="260" rx="8" fill="#00000020"/> <!-- Headers --> <text x="345" y="185" font-family="sans-serif" font-size="11" font-weight="700" fill="#94a3b8">METRIC</text> <text x="430" y="185" font-family="sans-serif" font-size="11" font-weight="700" fill="#38bdf8">PARAM (Gk)</text> <text x="510" y="185" font-family="sans-serif" font-size="11" font-weight="700" fill="#f59e0b">STAT (Lat)</text> <line x1="335" y1="195" x2="565" y2="195" stroke="#ffffff15" stroke-width="1"/> <!-- Row: Mean --> <text x="345" y="225" font-family="sans-serif" font-size="13" fill="#f8fafc">Mean</text> <text x="445" y="225" font-family="serif" font-size="18" fill="#38bdf8" text-anchor="middle">μ</text> <text x="525" y="225" font-family="serif" font-size="16" fill="#f59e0b" text-anchor="middle">x̄</text> <!-- Row: Std Dev --> <text x="345" y="265" font-family="sans-serif" font-size="13" fill="#f8fafc">Std Dev</text> <text x="445" y="265" font-family="serif" font-size="18" fill="#38bdf8" text-anchor="middle">σ</text> <text x="525" y="265" font-family="serif" font-size="16" fill="#f59e0b" text-anchor="middle">s</text> <!-- Row: Proportion --> <text x="345" y="305" font-family="sans-serif" font-size="13" fill="#f8fafc">Prop.</text> <text x="445" y="305" font-family="serif" font-size="18" fill="#38bdf8" text-anchor="middle">π</text> <text x="525" y="305" font-family="serif" font-size="16" fill="#f59e0b" text-anchor="middle">p̂</text> <!-- Estimation Arrow --> <path d="M525 330 Q450 380 375 330" fill="none" stroke="#e879f9" stroke-width="2" stroke-dasharray="4 2"/> <text x="450" y="385" text-anchor="middle" font-family="sans-serif" font-size="12" font-style="italic" fill="#e879f9">Estimation Process</text> <text x="450" y="405" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">Using sample to guess truth</text> <!-- Panel 3: Data Ontology --> <rect x="600" y="110" width="270" height="340" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="735" y="140" text-anchor="middle" font-family="sans-serif" font-size="18" font-weight="700" fill="#fbbf24">III. Data Types</text> <!-- Qualitative --> <rect x="620" y="165" width="230" height="60" rx="8" fill="#ffffff05" stroke="#38bdf830"/> <circle cx="645" cy="195" r="12" fill="#38bdf820" stroke="#38bdf8"/> <text x="645" y="199" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#38bdf8">A</text> <text x="670" y="188" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">Qualitative</text> <text x="670" y="205" font-family="sans-serif" font-size="11" fill="#94a3b8">Labels, Categories, Names</text> <!-- Quantitative --> <rect x="620" y="240" width="230" height="180" rx="8" fill="#ffffff05" stroke="#f59e0b30"/> <circle cx="645" cy="270" r="12" fill="#f59e0b20" stroke="#f59e0b"/> <text x="645" y="274" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="bold" fill="#f59e0b">#</text> <text x="670" y="265" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">Quantitative</text> <!-- Sub-types --> <line x1="645" y1="285" x2="645" y2="380" stroke="#f59e0b30" stroke-width="1"/> <circle cx="660" cy="320" r="4" fill="#f59e0b"/> <text x="675" y="325" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Discrete</text> <text x="675" y="340" font-family="sans-serif" font-size="10" fill="#94a3b8">Countable (e.g. 1, 2, 3)</text> <circle cx="660" cy="375" r="4" fill="#f59e0b"/> <text x="675" y="380" font-family="sans-serif" font-size="13" font-weight="600" fill="#f8fafc">Continuous</text> <text x="675" y="395" font-family="sans-serif" font-size="10" fill="#94a3b8">Measurable (e.g. 1.75m)</text> <!-- Footer Insight --> <rect x="30" y="470" width="840" height="60" rx="12" fill="#f59e0b10" stroke="#f59e0b40"/> <path d="M50 500 L70 500 M60 490 L60 510" stroke="#f59e0b" stroke-width="2" opacity="0.5"/> <text x="90" y="505" font-family="sans-serif" font-size="14" fill="#f8fafc"> <tspan font-weight="bold" fill="#f59e0b">KEY INSIGHT:</tspan> Statistics is the science of extracting meaning from <tspan fill="#e879f9">noise</tspan> by understanding <tspan fill="#38bdf8">variation</tspan>. </text> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="#e879f9" fill-opacity="0.1"/> <circle cx="850" cy="50" r="15" fill="#e879f9" fill-opacity="0.2"/> </svg>Sampling and Data image 1Sampling and Data - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/sampling-and-data/svg/1Sampling and Data diagram 1Sampling and Data - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/sampling-and-data/svg/2Sampling and Data diagram 2Sampling and Data - Introductory Statistics - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="-0.5">DESCRIPTIVE STATISTICS</text> <text x="40" y="85" font-family="sans-serif" font-size="14" fill="#94a3b8" font-weight="400">The Foundational Layer of Data Characterization &amp; Summarization</text> <rect x="40" y="105" width="180" height="4" fill="url(#accentGrad)" rx="2"/> <!-- Main Central Visual: The Distribution Curve --> <g transform="translate(250, 140)"> <rect width="400" height="260" rx="24" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="200" y="35" font-family="sans-serif" font-size="16" font-weight="600" fill="#f8fafc" text-anchor="middle">THE ANATOMY OF A DISTRIBUTION</text> <!-- Bell Curve Path --> <path d="M 50 220 Q 120 220 160 140 T 200 60 T 240 140 T 350 220" fill="none" stroke="#38bdf8" stroke-width="3" filter="url(#glow)"/> <!-- Central Lines --> <line x1="200" y1="60" x2="200" y2="220" stroke="#f59e0b" stroke-width="2" stroke-dasharray="4 2"/> <circle cx="200" cy="60" r="4" fill="#f59e0b"/> <text x="205" y="80" font-family="sans-serif" font-size="11" fill="#f59e0b" font-weight="bold">MEAN / MEDIAN / MODE</text> <!-- Dispersion Arrows --> <path d="M 140 160 L 260 160" stroke="#e879f9" stroke-width="1.5" marker-start="url(#arrow)" marker-end="url(#arrow)"/> <text x="200" y="155" font-family="sans-serif" font-size="10" fill="#e879f9" text-anchor="middle" font-weight="bold">STANDARD DEVIATION (σ)</text> <!-- Baseline --> <line x1="40" y1="220" x2="360" y2="220" stroke="#94a3b8" stroke-width="1"/> <!-- Small Data Points --> <circle cx="80" cy="220" r="3" fill="#38bdf8" opacity="0.6"/> <circle cx="110" cy="220" r="3" fill="#38bdf8" opacity="0.6"/> <circle cx="290" cy="220" r="3" fill="#38bdf8" opacity="0.6"/> <circle cx="330" cy="220" r="3" fill="#e879f9" opacity="0.9"/> <!-- Outlier --> <text x="330" y="235" font-family="sans-serif" font-size="9" fill="#e879f9" text-anchor="middle">OUTLIER</text> </g> <!-- Left Panel: Central Tendency --> <g transform="translate(40, 140)"> <rect width="190" height="380" rx="16" fill="#ffffff10" stroke="#ffffff10"/> <text x="20" y="35" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">CENTRAL TENDENCY</text> <!-- Mean Section --> <g transform="translate(20, 60)"> <rect width="30" height="30" rx="6" fill="#38bdf820"/> <path d="M 8 22 L 22 22 M 15 8 L 15 22" stroke="#38bdf8" stroke-width="2"/> <text x="40" y="15" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">MEAN (Average)</text> <text x="40" y="30" font-family="sans-serif" font-size="11" fill="#94a3b8">The balance point. Sensitive</text> <text x="40" y="42" font-family="sans-serif" font-size="11" fill="#94a3b8">to extreme outliers.</text> </g> <!-- Median Section --> <g transform="translate(20, 135)"> <rect width="30" height="30" rx="6" fill="#f59e0b20"/> <path d="M 8 15 L 22 15 M 15 8 L 15 22" stroke="#f59e0b" stroke-width="2" transform="rotate(45 15 15)"/> <text x="40" y="15" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">MEDIAN (Middle)</text> <text x="40" y="30" font-family="sans-serif" font-size="11" fill="#94a3b8">The robust center. Splits</text> <text x="40" y="42" font-family="sans-serif" font-size="11" fill="#94a3b8">data into two equal halves.</text> </g> <!-- Mode Section --> <g transform="translate(20, 210)"> <rect width="30" height="30" rx="6" fill="#e879f920"/> <path d="M 10 22 L 10 12 M 15 22 L 15 8 M 20 22 L 20 16" stroke="#e879f9" stroke-width="2"/> <text x="40" y="15" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">MODE (Frequent)</text> <text x="40" y="30" font-family="sans-serif" font-size="11" fill="#94a3b8">The most common value.</text> <text x="40" y="42" font-family="sans-serif" font-size="11" fill="#94a3b8">Works for categories.</text> </g> <!-- Formula Box --> <rect x="15" y="280" width="160" height="80" rx="8" fill="#00000030"/> <text x="25" y="305" font-family="serif" font-style="italic" font-size="16" fill="#f8fafc">x̄ = Σ x / n</text> <text x="25" y="330" font-family="sans-serif" font-size="10" fill="#94a3b8">"The arithmetic mean is the</text> <text x="25" y="342" font-family="sans-serif" font-size="10" fill="#94a3b8">sum of parts over count."</text> </g> <!-- Right Panel: Dispersion --> <g transform="translate(670, 140)"> <rect width="190" height="380" rx="16" fill="#ffffff10" stroke="#ffffff10"/> <text x="20" y="35" font-family="sans-serif" font-size="18" font-weight="700" fill="#e879f9">DISPERSION</text> <!-- Variance --> <g transform="translate(20, 60)"> <text x="0" y="15" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">VARIANCE (s²)</text> <text x="0" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Average squared distance</text> <text x="0" y="44" font-family="sans-serif" font-size="11" fill="#94a3b8">from the mean.</text> </g> <!-- Std Dev --> <g transform="translate(20, 135)"> <text x="0" y="15" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">STD. DEVIATION (σ)</text> <text x="0" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">Square root of variance.</text> <text x="0" y="44" font-family="sans-serif" font-size="11" fill="#94a3b8">Returns to original units.</text> </g> <!-- IQR --> <g transform="translate(20, 210)"> <text x="0" y="15" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">RANGE &amp; IQR</text> <text x="0" y="32" font-family="sans-serif" font-size="11" fill="#94a3b8">The 'width' of the data.</text> <text x="0" y="44" font-family="sans-serif" font-size="11" fill="#94a3b8">IQR = Q3 - Q1</text> </g> <!-- Visual Aid: Spread --> <g transform="translate(20, 280)"> <rect width="150" height="80" rx="8" fill="#00000030"/> <line x1="20" y1="40" x2="130" y2="40" stroke="#94a3b8" stroke-width="1"/> <rect x="45" y="30" width="60" height="20" fill="#e879f940" stroke="#e879f9" stroke-width="1"/> <line x1="75" y1="30" x2="75" y2="50" stroke="#f8fafc" stroke-width="2"/> <text x="75" y="70" font-family="sans-serif" font-size="10" fill="#94a3b8" text-anchor="middle">Box Plot Representation</text> </g> </g> <!-- Bottom Banner: The Sanity Check --> <g transform="translate(250, 420)"> <rect width="400" height="100" rx="16" fill="#f59e0b15" stroke="#f59e0b40"/> <circle cx="40" cy="50" r="20" fill="#f59e0b"/> <text x="40" y="56" font-family="sans-serif" font-size="20" font-weight="900" fill="#0f172a" text-anchor="middle">!</text> <text x="75" y="45" font-family="sans-serif" font-size="16" font-weight="700" fill="#f59e0b">THE "SANITY CHECK" PHASE</text> <text x="75" y="65" font-family="sans-serif" font-size="12" fill="#f8fafc">Avoid "Garbage In, Garbage Out" (GIGO). 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Introductory Statistics - diagram 3https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/probability-topics/svg/1Probability Topics diagram 1Probability Topics - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/probability-topics/svg/2Probability Topics diagram 2Probability Topics - Introductory Statistics - diagram 2https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/probability-topics/svg/3Probability Topics diagram 3Probability Topics - Introductory Statistics - diagram 3https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/discrete-random-variables/svg/1Discrete Random Variables diagram 1Discrete Random Variables - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/discrete-random-variables/svg/2Discrete Random Variables diagram 2Discrete Random Variables - Introductory Statistics - diagram 2https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/discrete-random-variables/svg/3Discrete Random Variables diagram 3Discrete Random Variables - Introductory Statistics - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#818cf8"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">CONTINUOUS RANDOM VARIABLES</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">The Mathematics of Infinite Precision and Density</text> <line x1="350" y1="90" x2="550" y2="90" stroke="url(#accentGrad)" stroke-width="2" stroke-linecap="round"/> <!-- Left Card: Discrete vs Continuous --> <rect x="30" y="110" width="260" height="420" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="160" y="145" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">THE FUNDAMENTAL SHIFT</text> <!-- Comparison Icons --> <g transform="translate(65, 170)"> <rect width="80" height="80" rx="8" fill="#ffffff05" stroke="#94a3b8" stroke-dasharray="4 2"/> <text x="40" y="45" text-anchor="middle" font-family="serif" font-size="36" fill="#94a3b8">Σ</text> <text x="40" y="95" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#94a3b8">Discrete Sum</text> </g> <g transform="translate(175, 170)"> <rect width="80" height="80" rx="8" fill="#38bdf815" stroke="#38bdf8"/> <text x="40" y="45" text-anchor="middle" font-family="serif" font-size="36" fill="#38bdf8">∫</text> <text x="40" y="95" text-anchor="middle" font-family="sans-serif" font-size="12" fill="#38bdf8">Continuous</text> </g> <g font-family="sans-serif" font-size="13" fill="#f8fafc"> <text x="50" y="300">• Countable Outcomes</text> <text x="50" y="325" fill="#94a3b8" font-size="11">vs. Uncountable Intervals</text> <text x="50" y="360">• Point Probability P(X=x)</text> <text x="50" y="385" fill="#94a3b8" font-size="11">vs. Density Probability P(a&lt;X&lt;b)</text> <text x="50" y="420">• Bar Charts &amp; PMFs</text> <text x="50" y="445" fill="#94a3b8" font-size="11">vs. Smooth Density Curves (PDF)</text> </g> <!-- Middle Card: The PDF Geometry --> <rect x="310" y="110" width="280" height="420" rx="16" fill="#ffffff10" stroke="#ffffff20" stroke-width="1"/> <text x="450" y="145" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">GEOMETRY OF DENSITY</text> <!-- PDF Curve Illustration --> <g transform="translate(330, 180)"> <!-- Axis --> <line x1="10" y1="140" x2="230" y2="140" stroke="#94a3b8" stroke-width="1"/> <line x1="10" y1="20" x2="10" y2="140" stroke="#94a3b8" stroke-width="1"/> <!-- Shaded Area --> <path d="M 80 140 L 80 75 Q 120 40 160 85 L 160 140 Z" fill="#f59e0b40" /> <!-- Curve --> <path d="M 20 130 Q 60 120 90 60 T 160 90 T 220 135" fill="none" stroke="#f59e0b" stroke-width="3" filter="glow"/> <!-- Labels --> <text x="80" y="155" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">a</text> <text x="160" y="155" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">b</text> <text x="120" y="110" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f59e0b">Area = P(a ≤ X ≤ b)</text> <text x="220" y="50" text-anchor="end" font-family="serif" font-size="14" fill="#f8fafc">f(x)</text> </g> <g font-family="sans-serif" font-size="12" fill="#cbd5e1"> <text x="335" y="360" font-weight="bold" fill="#f8fafc">1. Non-negativity:</text> <text x="335" y="378">f(x) ≥ 0 for all x</text> <text x="335" y="410" font-weight="bold" fill="#f8fafc">2. Unit Area:</text> <text x="335" y="428">∫ f(x) dx = 1 (Total Probability)</text> <text x="335" y="460" font-weight="bold" fill="#f8fafc">3. The Zero Paradox:</text> <text x="335" y="478">P(X = exact value) = 0</text> <text x="335" y="494" font-size="10" fill="#94a3b8">Area of a single point is zero.</text> </g> <!-- Right Card: Uniform Distribution --> <rect x="610" y="110" width="260" height="420" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="740" y="145" text-anchor="middle" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">UNIFORM MODEL</text> <!-- Uniform Graphic --> <g transform="translate(640, 180)"> <rect x="30" y="40" width="140" height="80" fill="#e879f920" stroke="#e879f9" stroke-width="2" stroke-dasharray="2 2"/> <line x1="10" y1="120" x2="190" y2="120" stroke="#94a3b8" stroke-width="1"/> <text x="30" y="135" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">a</text> <text x="170" y="135" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">b</text> <text x="25" y="45" text-anchor="end" font-family="serif" font-size="10" fill="#e879f9">1/(b-a)</text> <text x="100" y="85" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">Equal Likelihood</text> </g> <rect x="630" y="340" width="220" height="160" rx="8" fill="#00000030"/> <g font-family="monospace" font-size="12" fill="#e879f9"> <text x="645" y="365">Mean: (a + b) / 2</text> <text x="645" y="390" fill="#94a3b8">Var: (b - a)² / 12</text> <text x="645" y="415" fill="#94a3b8">CDF: (x - a) / (b - a)</text> </g> <text x="645" y="450" font-family="sans-serif" font-size="11" fill="#f8fafc" font-weight="bold">Use Case:</text> <text x="645" y="468" font-family="sans-serif" font-size="11" fill="#94a3b8">Wait times, random number</text> <text x="645" y="482" font-family="sans-serif" font-size="11" fill="#94a3b8">generation, and quantization</text> <text x="645" y="496" font-family="sans-serif" font-size="11" fill="#94a3b8">error modeling.</text> <!-- Decorative Footer Elements --> <circle cx="40" cy="40" r="20" fill="#38bdf8" fill-opacity="0.1"/> <circle cx="860" cy="520" r="30" fill="#e879f9" fill-opacity="0.1"/> <path d="M 820 40 L 850 70 M 850 40 L 820 70" stroke="#ffffff10" stroke-width="2"/> </svg>Continuous Random Variables image 1Continuous Random Variables - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/continuous-random-variables/svg/1Continuous Random Variables diagram 1Continuous Random Variables - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/continuous-random-variables/svg/2Continuous Random Variables diagram 2Continuous Random Variables - Introductory Statistics - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Definitions: Gradients, Filters, and Patterns --> <defs> <linearGradient id="bgGradient" x1="0%" y1="0%" x2="0%" y2="100%"> <stop offset="0%" stop-color="#0f172a" /> <stop offset="100%" stop-color="#1e1b4b" /> </linearGradient> <pattern id="dotPattern" x="0" y="0" width="30" height="30" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff08" /> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <linearGradient id="curveGradient" x1="0%" y1="0%" x2="100%" y2="0%"> <stop offset="0%" stop-color="#38bdf8" /> <stop offset="50%" stop-color="#e879f9" /> <stop offset="100%" stop-color="#f59e0b" /> </linearGradient> </defs> <!-- Background Layer --> <rect width="900" height="560" fill="url(#bgGradient)" /> <rect width="900" height="560" fill="url(#dotPattern)" /> <!-- Header Section --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="32" font-weight="800" letter-spacing="1">THE NORMAL DISTRIBUTION</text> <text x="450" y="75" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="400" letter-spacing="2">THE GAUSSIAN FOUNDATION OF STATISTICS</text> <line x1="350" y1="90" x2="550" y2="90" stroke="#ffffff20" stroke-width="1" /> <!-- Main Visualization Area: The Bell Curve --> <!-- Shaded Areas for Empirical Rule --> <path d="M 150,420 Q 300,420 350,370 T 450,180 T 550,370 Q 600,420 750,420 L 750,420 L 150,420 Z" fill="#ffffff05" /> <!-- 99.7% Zone --> <path d="M 210,420 Q 300,420 350,370 T 450,180 T 550,370 Q 600,420 690,420 Z" fill="#f59e0b10" /> <!-- 95% Zone --> <path d="M 290,420 Q 330,420 370,330 T 450,180 T 530,330 Q 570,420 610,420 Z" fill="#e879f915" /> <!-- 68% Zone --> <path d="M 370,420 Q 390,420 410,260 T 450,180 T 490,260 Q 510,420 530,420 Z" fill="#38bdf825" /> <!-- The Curve Line --> <path d="M 150,420 Q 300,420 350,370 T 450,180 T 550,370 Q 600,420 750,420" fill="none" stroke="url(#curveGradient)" stroke-width="4" filter="url(#glow)" /> <!-- Axis and Labels --> <line x1="120" y1="420" x2="780" y2="420" stroke="#94a3b8" stroke-width="2" stroke-linecap="round" /> <text x="450" y="445" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="18" font-style="italic">μ (Mean)</text> <!-- Empirical Rule Callouts --> <g font-family="sans-serif" font-weight="bold" text-anchor="middle"> <text x="450" y="320" fill="#38bdf8" font-size="16">68.2%</text> <text x="450" y="335" fill="#38bdf8" font-size="10" font-weight="normal">±1σ</text> <text x="330" y="390" fill="#e879f9" font-size="14">95.4%</text> <text x="330" y="402" fill="#e879f9" font-size="9" font-weight="normal">±2σ</text> <text x="570" y="390" fill="#e879f9" font-size="14">95.4%</text> <text x="570" y="402" fill="#e879f9" font-size="9" font-weight="normal">±2σ</text> </g> <!-- Left Panel: Parameters --> <rect x="30" y="130" width="200" height="260" rx="16" fill="#ffffff08" stroke="#ffffff15" /> <circle cx="55" cy="160" r="12" fill="#38bdf8" /> <text x="55" y="165" text-anchor="middle" fill="#0f172a" font-family="sans-serif" font-size="12" font-weight="bold">1</text> <text x="75" y="165" fill="#f8fafc" font-family="sans-serif" font-size="16" font-weight="bold">Parameters</text> <text x="50" y="200" fill="#38bdf8" font-family="serif" font-size="20" font-weight="bold">μ</text> <text x="75" y="200" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="bold">Mean</text> <text x="50" y="218" fill="#94a3b8" font-family="sans-serif" font-size="11">The center of the bell. Where</text> <text x="50" y="232" fill="#94a3b8" font-family="sans-serif" font-size="11">Mean = Median = Mode.</text> <text x="50" y="270" fill="#e879f9" font-family="serif" font-size="20" font-weight="bold">σ</text> <text x="75" y="270" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="bold">Std. Deviation</text> <text x="50" y="288" fill="#94a3b8" font-family="sans-serif" font-size="11">The spread. Larger σ creates</text> <text x="50" y="302" fill="#94a3b8" font-family="sans-serif" font-size="11">a wider, flatter curve.</text> <rect x="50" y="325" width="160" height="45" rx="8" fill="#00000030" /> <text x="130" y="345" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="11">f(x|μ,σ) = [1/σ√(2π)]</text> <text x="130" y="360" text-anchor="middle" fill="#f8fafc" font-family="serif" font-size="11">· e^[-(x-μ)²/2σ²]</text> <!-- Right Panel: Standardization --> <rect x="670" y="130" width="200" height="260" rx="16" fill="#ffffff08" stroke="#ffffff15" /> <circle cx="695" cy="160" r="12" fill="#e879f9" /> <text x="695" y="165" text-anchor="middle" fill="#0f172a" font-family="sans-serif" font-size="12" font-weight="bold">2</text> <text x="715" y="165" fill="#f8fafc" font-family="sans-serif" font-size="16" font-weight="bold">Z-Scores</text> <text x="690" y="200" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="bold">Standardization</text> <text x="690" y="218" fill="#94a3b8" font-family="sans-serif" font-size="11">Converting any normal curve</text> <text x="690" y="232" fill="#94a3b8" font-family="sans-serif" font-size="11">to μ=0 and σ=1.</text> <path d="M 710,260 L 830,260 M 770,260 L 770,310" stroke="#ffffff20" stroke-width="1" /> <text x="770" y="340" text-anchor="middle" fill="#f59e0b" font-family="serif" font-size="24" font-weight="bold">z = (x - μ) / σ</text> <text x="770" y="365" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="11">The distance from the mean</text> <text x="770" y="378" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="11">in units of standard deviation.</text> <!-- Bottom Panel: Real World Examples --> <rect x="30" y="470" width="840" height="70" rx="16" fill="#ffffff05" stroke="#ffffff10" /> <text x="60" y="510" fill="#f59e0b" font-family="sans-serif" font-size="14" font-weight="bold">COMMON APPLICATIONS:</text> <g transform="translate(250, 495)"> <circle cx="0" cy="10" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="1" /> <path d="M -5,15 L -5,5 L 5,5 L 5,15" fill="none" stroke="#38bdf8" stroke-width="1.5" /> <text x="25" y="15" fill="#f8fafc" font-family="sans-serif" font-size="12">Biological Heights</text> </g> <g transform="translate(450, 495)"> <circle cx="0" cy="10" r="15" fill="#e879f920" stroke="#e879f9" stroke-width="1" /> <path d="M -6,10 L 6,10 M 0,4 L 0,16" fill="none" stroke="#e879f9" stroke-width="1.5" /> <text x="25" y="15" fill="#f8fafc" font-family="sans-serif" font-size="12">Measurement Errors</text> </g> <g transform="translate(670, 495)"> <circle cx="0" cy="10" r="15" fill="#f59e0b20" stroke="#f59e0b" stroke-width="1" /> <path d="M -5,10 Q 0,0 5,10 T 15,10" fill="none" stroke="#f59e0b" stroke-width="1.5" /> <text x="25" y="15" fill="#f8fafc" font-family="sans-serif" font-size="12">IQ &amp; Test Scores</text> </g> <!-- Decorative elements --> <circle cx="850" cy="50" r="40" fill="#f59e0b05" /> <circle cx="850" cy="50" r="20" fill="#f59e0b10" /> <circle cx="50" cy="510" r="30" fill="#38bdf805" /> </svg>The Normal Distribution image 1The Normal Distribution - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/the-normal-distribution/svg/1The Normal Distribution diagram 1The Normal Distribution - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/the-normal-distribution/svg/2The Normal Distribution diagram 2The Normal Distribution - Introductory Statistics - diagram 2https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/the-normal-distribution/svg/3The Normal Distribution diagram 3The Normal Distribution - Introductory Statistics - diagram 3<svg viewBox="0 0 900 560" xmlns="http://www.w3.org/2000/svg"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <!-- Decorative Grid --> <g stroke="#ffffff08" stroke-width="1"> <path d="M 0 100 H 900 M 0 200 H 900 M 0 300 H 900 M 0 400 H 900 M 0 500 H 900"/> <path d="M 100 0 V 560 M 200 0 V 560 M 300 0 V 560 M 400 0 V 560 M 500 0 V 560 M 600 0 V 560 M 700 0 V 560 M 800 0 V 560"/> </g> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">The Central Limit Theorem</text> <text x="40" y="85" font-family="sans-serif" font-size="16" fill="#94a3b8" letter-spacing="1">THE BRIDGE FROM CHAOS TO ORDER</text> <rect x="40" y="105" width="120" height="4" rx="2" fill="url(#accentGrad)"/> <!-- Main Conceptual Flow --> <!-- Step 1: Population --> <rect x="40" y="140" width="250" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="175" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">1. The Population</text> <text x="60" y="195" font-family="sans-serif" font-size="12" fill="#94a3b8">Any distribution shape (skewed, uniform, discrete)</text> <!-- Skewed Distribution Graphic --> <path d="M 70 330 Q 80 230 120 230 T 260 330" fill="none" stroke="#f59e0b" stroke-width="3" filter="url(#glow)"/> <line x1="70" y1="330" x2="260" y2="330" stroke="#475569" stroke-width="1"/> <text x="70" y="350" font-family="serif" font-style="italic" font-size="14" fill="#f59e0b">μ</text> <text x="160" y="260" font-family="sans-serif" font-size="11" fill="#f8fafc" opacity="0.8">Non-Normal Data</text> <!-- Arrow 1 --> <path d="M 305 260 L 335 260" stroke="#38bdf8" stroke-width="2" fill="none" marker-end="url(#arrowhead)"/> <!-- Step 2: Sampling --> <rect x="325" y="140" width="250" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="345" y="175" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">2. Sampling Process</text> <text x="345" y="195" font-family="sans-serif" font-size="12" fill="#94a3b8">Take repeated samples of size n</text> <!-- Sampling Animation Concept --> <g transform="translate(365, 230)"> <circle cx="0" cy="0" r="15" fill="#38bdf822" stroke="#38bdf8" stroke-width="1"/> <text x="-8" y="5" font-family="sans-serif" font-size="10" fill="#38bdf8">n₁</text> <circle cx="40" cy="20" r="15" fill="#38bdf822" stroke="#38bdf8" stroke-width="1"/> <text x="32" y="25" font-family="sans-serif" font-size="10" fill="#38bdf8">n₂</text> <circle cx="80" cy="-10" r="15" fill="#38bdf822" stroke="#38bdf8" stroke-width="1"/> <text x="72" y="-5" font-family="sans-serif" font-size="10" fill="#38bdf8">n₃</text> <circle cx="120" cy="30" r="15" fill="#38bdf822" stroke="#38bdf8" stroke-width="1"/> <text x="112" y="35" font-family="sans-serif" font-size="10" fill="#38bdf8">n...</text> <path d="M 0 60 Q 85 100 170 60" fill="none" stroke="#38bdf8" stroke-dasharray="4 2" opacity="0.5"/> <text x="35" y="105" font-family="sans-serif" font-size="13" font-weight="bold" fill="#f8fafc">Calculate Means (x̄)</text> </g> <!-- Arrow 2 --> <path d="M 590 260 L 620 260" stroke="#e879f9" stroke-width="2" fill="none"/> <!-- Step 3: Result --> <rect x="610" y="140" width="250" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="630" y="175" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">3. The Normal Curve</text> <text x="630" y="195" font-family="sans-serif" font-size="12" fill="#94a3b8">The distribution of x̄ becomes Gaussian</text> <!-- Bell Curve Graphic --> <path d="M 640 330 Q 735 180 830 330" fill="none" stroke="#e879f9" stroke-width="3" filter="url(#glow)"/> <line x1="640" y1="330" x2="830" y2="330" stroke="#475569" stroke-width="1"/> <line x1="735" y1="330" x2="735" y2="210" stroke="#e879f9" stroke-dasharray="2 2"/> <text x="730" y="350" font-family="serif" font-style="italic" font-size="14" fill="#e879f9">μ</text> <text x="745" y="240" font-family="sans-serif" font-size="11" fill="#f8fafc">n ≥ 30</text> <!-- Bottom Info Panels --> <!-- LLN vs CLT --> <rect x="40" y="400" width="400" height="130" rx="16" fill="#ffffff05" stroke="#ffffff10"/> <text x="60" y="430" font-family="sans-serif" font-weight="700" font-size="16" fill="#f8fafc">LLN vs. CLT</text> <text x="60" y="455" font-family="sans-serif" font-size="12" fill="#94a3b8">Law of Large Numbers (LLN):</text> <text x="60" y="472" font-family="sans-serif" font-size="13" fill="#f8fafc">The sample mean converges to the population mean.</text> <text x="60" y="495" font-family="sans-serif" font-size="12" fill="#94a3b8">Central Limit Theorem (CLT):</text> <text x="60" y="512" font-family="sans-serif" font-size="13" fill="#f8fafc">The distribution of means takes a specific shape.</text> <!-- Standard Error Panel --> <rect x="460" y="400" width="400" height="130" rx="16" fill="#0ea5e915" stroke="#38bdf833"/> <text x="480" y="430" font-family="sans-serif" font-weight="700" font-size="16" fill="#38bdf8">The Square Root Law</text> <text x="480" y="465" font-family="serif" font-size="24" fill="#f8fafc">SE = σ / √n</text> <text x="480" y="495" font-family="sans-serif" font-size="12" fill="#94a3b8">To double your precision (halve the error),</text> <text x="480" y="512" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">you must quadruple your sample size.</text> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#ffffff10" stroke-width="8"/> <circle cx="850" cy="50" r="15" fill="#e879f922"/> </svg>The Central Limit Theorem image 1The Central Limit Theorem - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/the-central-limit-theorem/svg/1The Central Limit Theorem diagram 1The Central Limit Theorem - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/the-central-limit-theorem/svg/2The Central Limit Theorem diagram 2The Central Limit Theorem - Introductory Statistics - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#334155" fill-opacity="0.5"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Title Section --> <text x="450" y="55" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">CONFIDENCE INTERVALS</text> <text x="450" y="80" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">Quantifying Uncertainty in Frequentist Statistics</text> <line x1="380" y1="95" x2="520" y2="95" stroke="#38bdf8" stroke-width="2" stroke-linecap="round"/> <!-- Left Panel: The Anatomy --> <rect x="40" y="120" width="260" height="280" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">THE ANATOMY</text> <!-- Anatomy Diagram --> <g transform="translate(60, 210)"> <line x1="0" y1="0" x2="220" y2="0" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4 2"/> <circle cx="110" cy="0" r="6" fill="#38bdf8" filter="url(#glow)"/> <path d="M 30 -10 L 30 10 M 30 0 L 190 0 M 190 -10 L 190 10" stroke="#f8fafc" stroke-width="3" fill="none"/> <text x="110" y="-15" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#38bdf8" font-weight="bold">POINT ESTIMATE (x̄)</text> <text x="110" y="35" text-anchor="middle" font-family="sans-serif" font-size="11" fill="#f8fafc">MARGIN OF ERROR (EBM)</text> <path d="M 110 20 L 190 20" stroke="#f8fafc" stroke-width="1" marker-end="url(#arrow)"/> <path d="M 110 20 L 30 20" stroke="#f8fafc" stroke-width="1"/> </g> <text x="60" y="300" font-family="sans-serif" font-size="12" fill="#94a3b8" width="220"> <tspan x="60" dy="1.4em">• Confidence Level (1 - α)</tspan> <tspan x="60" dy="1.4em">• Critical Value (z* or t*)</tspan> <tspan x="60" dy="1.4em">• Standard Error (SE)</tspan> <tspan x="60" dy="1.4em">• Sample Size (n)</tspan> </text> <!-- Center Panel: The Frequentist Interpretation --> <rect x="320" y="120" width="260" height="280" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="340" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">THE INTERPRETATION</text> <!-- Frequentist Visualization --> <g transform="translate(450, 180)"> <line x1="0" y1="0" x2="0" y2="180" stroke="#f59e0b" stroke-width="2" stroke-dasharray="2 2"/> <text x="5" y="10" font-family="sans-serif" font-size="10" fill="#f59e0b">TRUE PARAMETER (μ)</text> <!-- Intervals --> <g stroke-width="1.5"> <line x1="-40" y1="30" x2="30" y2="30" stroke="#38bdf8"/> <line x1="-20" y1="50" x2="50" y2="50" stroke="#38bdf8"/> <line x1="-60" y1="70" x2="10" y2="70" stroke="#38bdf8"/> <!-- The Miss --> <line x1="10" y1="90" x2="80" y2="90" stroke="#e879f9" stroke-width="2.5"/> <circle cx="45" cy="90" r="3" fill="#e879f9"/> <line x1="-30" y1="110" x2="40" y2="110" stroke="#38bdf8"/> <line x1="-50" y1="130" x2="20" y2="130" stroke="#38bdf8"/> <line x1="-10" y1="150" x2="60" y2="150" stroke="#38bdf8"/> </g> </g> <text x="340" y="365" font-family="sans-serif" font-size="11" fill="#94a3b8"> <tspan x="340" dy="1.2em">If we repeat sampling 100 times,</tspan> <tspan x="340" dy="1.2em">95 intervals will capture the</tspan> <tspan x="340" dy="1.2em">true population parameter.</tspan> </text> <!-- Right Panel: Z vs T Distribution --> <rect x="600" y="120" width="260" height="280" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">Z vs. T DISTRIBUTIONS</text> <!-- Curve Comparison --> <g transform="translate(630, 250)"> <!-- Z Curve (Normal) --> <path d="M 0 0 Q 100 -120 200 0" stroke="#38bdf8" stroke-width="2" fill="none"/> <!-- T Curve (Heavier Tails) --> <path d="M 0 0 Q 100 -80 200 0" stroke="#e879f9" stroke-width="2" fill="none" stroke-dasharray="4 2"/> <line x1="0" y1="0" x2="200" y2="0" stroke="#94a3b8" stroke-width="1"/> <text x="100" y="-100" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#38bdf8">Z (Normal)</text> <text x="100" y="-55" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#e879f9">T (Heavier Tails)</text> </g> <text x="620" y="300" font-family="sans-serif" font-size="12" fill="#94a3b8"> <tspan x="620" dy="1.4em" fill="#f8fafc" font-weight="bold">Use Z-Distribution if:</tspan> <tspan x="620" dy="1.4em">Population σ is known.</tspan> <tspan x="620" dy="1.8em" fill="#f8fafc" font-weight="bold">Use T-Distribution if:</tspan> <tspan x="620" dy="1.4em">σ is unknown (use sample s).</tspan> <tspan x="620" dy="1.4em">Essential for small samples (n &lt; 30).</tspan> </text> <!-- Bottom Panel: The Formulas --> <rect x="40" y="420" width="820" height="110" rx="16" fill="#ffffff10" stroke="#ffffff20"/> <g transform="translate(80, 455)"> <text x="0" y="0" font-family="serif" font-size="20" fill="#f8fafc">CI = x̄ ± z* · (σ / √n)</text> <text x="0" y="25" font-family="sans-serif" font-size="12" fill="#38bdf8">Standard Normal Case</text> </g> <line x1="450" y1="440" x2="450" y2="510" stroke="#ffffff20" stroke-width="1"/> <g transform="translate(500, 455)"> <text x="0" y="0" font-family="serif" font-size="20" fill="#f8fafc">CI = x̄ ± t* · (s / √n)</text> <text x="0" y="25" font-family="sans-serif" font-size="12" fill="#e879f9">Student's T Case (df = n - 1)</text> </g> <!-- Decorative Guinness Reference --> <text x="840" y="515" text-anchor="end" font-family="sans-serif" font-size="9" fill="#475569">Gosset's Brewery Method (1908)</text> <!-- Corner Accents --> <circle cx="40" cy="40" r="20" fill="#38bdf8" fill-opacity="0.1"/> <circle cx="860" cy="520" r="30" fill="#f59e0b" fill-opacity="0.05"/> </svg>Confidence Intervals image 1Confidence Intervals - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/confidence-intervals/svg/1Confidence Intervals diagram 1Confidence Intervals - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/confidence-intervals/svg/2Confidence Intervals diagram 2Confidence Intervals - Introductory Statistics - diagram 2https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/confidence-intervals/svg/3Confidence Intervals diagram 3Confidence Intervals - Introductory Statistics - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <filter id="glow" x="-20%" y="-20%" width="140%" height="140%"> <feGaussianBlur stdDeviation="3" result="blur" /> <feComposite in="SourceGraphic" in2="blur" operator="over" /> </filter> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Title Section --> <text x="450" y="50" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="32" font-weight="bold" letter-spacing="1">ONE-SAMPLE HYPOTHESIS TESTING</text> <text x="450" y="75" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="14" font-weight="300" letter-spacing="2">THE STATISTICAL BACKBONE OF SCIENTIFIC INFERENCE</text> <line x1="350" y1="85" x2="550" y2="85" stroke="#38bdf8" stroke-width="2" opacity="0.5"/> <!-- Top Row: The Framework --> <!-- Card 1: Hypotheses --> <rect x="40" y="110" width="260" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="60" y="140" fill="#f59e0b" font-family="sans-serif" font-size="18" font-weight="bold">01. THE FRAMEWORK</text> <g transform="translate(60, 165)"> <rect width="220" height="45" rx="8" fill="#ffffff05"/> <text x="10" y="18" fill="#f8fafc" font-family="sans-serif" font-size="13" font-weight="bold">H₀: Null Hypothesis</text> <text x="10" y="34" fill="#94a3b8" font-family="sans-serif" font-size="11">The status quo. Equality (=, ≤, ≥)</text> <circle cx="200" cy="22" r="6" fill="#f59e0b" opacity="0.8"/> </g> <g transform="translate(60, 220)"> <rect width="220" height="45" rx="8" fill="#ffffff05"/> <text x="10" y="18" fill="#38bdf8" font-family="sans-serif" font-size="13" font-weight="bold">Hₐ: Alternative Hypothesis</text> <text x="10" y="34" fill="#94a3b8" font-family="sans-serif" font-size="11">The research claim. Difference (≠, &lt;, &gt;)</text> <path d="M195 28 L200 18 L205 28 Z" fill="#38bdf8" opacity="0.8"/> </g> <!-- Card 2: Decision Calculus --> <rect x="320" y="110" width="260" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="340" y="140" fill="#e879f9" font-family="sans-serif" font-size="18" font-weight="bold">02. DECISION RULES</text> <path d="M360 230 Q450 160 540 230" stroke="#94a3b8" fill="none" stroke-width="2"/> <path d="M510 230 Q525 210 540 230 Z" fill="#e879f9" opacity="0.4"/> <text x="450" y="255" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="12">P-Value vs. Alpha (α)</text> <rect x="340" y="160" width="105" height="40" rx="6" fill="#fb718520" stroke="#fb718540"/> <text x="392" y="178" text-anchor="middle" fill="#fb7185" font-family="sans-serif" font-size="11" font-weight="bold">P ≤ α</text> <text x="392" y="192" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="10">Reject H₀</text> <rect x="455" y="160" width="105" height="40" rx="6" fill="#4ade8020" stroke="#4ade8040"/> <text x="507" y="178" text-anchor="middle" fill="#4ade80" font-family="sans-serif" font-size="11" font-weight="bold">P &gt; α</text> <text x="507" y="192" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="10">Fail to Reject</text> <!-- Card 3: Error Theory --> <rect x="600" y="110" width="260" height="180" rx="16" fill="#ffffff08" stroke="#ffffff15"/> <text x="620" y="140" fill="#2dd4bf" font-family="sans-serif" font-size="18" font-weight="bold">03. ERROR THEORY</text> <g transform="translate(620, 160)"> <!-- Matrix --> <rect x="0" y="0" width="220" height="100" rx="8" fill="#ffffff05"/> <line x1="110" y1="0" x2="110" y2="100" stroke="#ffffff10"/> <line x1="0" y1="50" x2="220" y2="50" stroke="#ffffff10"/> <text x="55" y="30" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="9">H₀ True</text> <text x="55" y="42" text-anchor="middle" fill="#fb7185" font-family="sans-serif" font-size="10" font-weight="bold">TYPE I ERROR</text> <text x="165" y="30" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="9">H₀ False</text> <text x="165" y="42" text-anchor="middle" fill="#4ade80" font-family="sans-serif" font-size="10" font-weight="bold">POWER (1-β)</text> <text x="55" y="80" text-anchor="middle" fill="#4ade80" font-family="sans-serif" font-size="10" font-weight="bold">CORRECT</text> <text x="165" y="80" text-anchor="middle" fill="#fb7185" font-family="sans-serif" font-size="10" font-weight="bold">TYPE II ERROR</text> </g> <!-- Bottom Section: Mechanics --> <rect x="40" y="310" width="820" height="210" rx="20" fill="#ffffff08" stroke="#ffffff15"/> <text x="70" y="345" fill="#38bdf8" font-family="sans-serif" font-size="20" font-weight="bold">MECHANICS: SELECTING THE TEST</text> <!-- Flowchart --> <g transform="translate(70, 370)"> <!-- Start --> <rect x="0" y="20" width="140" height="60" rx="10" fill="#ffffff10"/> <text x="70" y="45" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="12" font-weight="bold">Is σ known?</text> <text x="70" y="62" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="10">(Pop. Std Dev)</text> <!-- Arrows --> <path d="M140 50 L200 50" stroke="#38bdf8" stroke-width="2" fill="none" marker-end="url(#arrow)"/> <text x="170" y="40" text-anchor="middle" fill="#4ade80" font-family="sans-serif" font-size="10">YES</text> <path d="M70 80 L70 110 L200 110" stroke="#f59e0b" stroke-width="2" fill="none"/> <text x="100" y="105" text-anchor="middle" fill="#f59e0b" font-family="sans-serif" font-size="10">NO</text> <!-- Z-Test --> <rect x="200" y="20" width="220" height="60" rx="10" fill="#38bdf820" stroke="#38bdf8"/> <text x="215" y="45" fill="#38bdf8" font-family="sans-serif" font-size="14" font-weight="bold">One-Sample Z-Test</text> <text x="215" y="65" fill="#f8fafc" font-family="monospace" font-size="12">z = (x̄ - μ₀) / (σ/√n)</text> <!-- T-Test --> <rect x="200" y="90" width="220" height="60" rx="10" fill="#f59e0b20" stroke="#f59e0b"/> <text x="215" y="115" fill="#f59e0b" font-family="sans-serif" font-size="14" font-weight="bold">One-Sample T-Test</text> <text x="215" y="135" fill="#f8fafc" font-family="monospace" font-size="12">t = (x̄ - μ₀) / (s/√n)</text> <!-- Requirements Info --> <g transform="translate(460, 20)"> <rect width="300" height="130" rx="12" fill="#ffffff05"/> <text x="15" y="25" fill="#94a3b8" font-family="sans-serif" font-size="12" font-weight="bold">REQUIREMENTS &amp; ASSUMPTIONS</text> <circle cx="25" cy="50" r="3" fill="#38bdf8"/> <text x="40" y="54" fill="#f8fafc" font-family="sans-serif" font-size="11">Random Sampling from the population</text> <circle cx="25" cy="75" r="3" fill="#38bdf8"/> <text x="40" y="79" fill="#f8fafc" font-family="sans-serif" font-size="11">Independence of observations</text> <circle cx="25" cy="100" r="3" fill="#38bdf8"/> <text x="40" y="104" fill="#f8fafc" font-family="sans-serif" font-size="11">Normality (n &gt; 30 or normal population)</text> </g> </g> <!-- Footer --> <text x="860" y="540" text-anchor="end" fill="#ffffff20" font-family="sans-serif" font-size="10">STATISTICS WIKI // MODULE 04</text> <!-- Decorative Marker --> <defs> <marker id="arrow" markerWidth="10" markerHeight="10" refX="9" refY="5" orientation="auto"> <path d="M0,0 L10,5 L0,10 Z" fill="#38bdf8" /> </marker> </defs> </svg>Hypothesis Testing with One Sample image 1Hypothesis Testing with One Sample - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/hypothesis-testing-one-sample/svg/1Hypothesis Testing with One Sample diagram 1Hypothesis Testing with One Sample - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/hypothesis-testing-one-sample/svg/2Hypothesis Testing with One Sample diagram 2Hypothesis Testing with One Sample - Introductory Statistics - diagram 2https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/hypothesis-testing-one-sample/svg/3Hypothesis Testing with One Sample diagram 3Hypothesis Testing with One Sample - Introductory Statistics - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg-grad" x1="0%" y1="0%" x2="0%" y2="100%"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="30" height="30" patternUnits="userSpaceOnUse"> <path d="M 30 0 L 0 0 0 30" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background Layer --> <rect width="900" height="560" fill="url(#bg-grad)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Decorative Elements --> <circle cx="850" cy="50" r="100" fill="#38bdf8" fill-opacity="0.05"/> <circle cx="50" cy="510" r="80" fill="#e879f9" fill-opacity="0.05"/> <path d="M 0 100 Q 450 150 900 100" fill="none" stroke="#ffffff05" stroke-width="2"/> <!-- Header Section --> <text x="450" y="55" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">HYPOTHESIS TESTING WITH TWO SAMPLES</text> <text x="450" y="82" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">Determining statistical significance across comparative landscapes</text> <rect x="400" y="95" width="100" height="3" rx="1.5" fill="#f59e0b"/> <!-- Main Content Cards --> <!-- Card 1: Independent Samples --> <rect x="40" y="120" width="400" height="180" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="65" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">Independent T-Test</text> <text x="65" y="172" font-family="sans-serif" font-size="12" fill="#94a3b8">COMPARING UNRELATED GROUPS</text> <!-- Icon: Two Bell Curves --> <path d="M 70 260 Q 100 200 130 260" fill="none" stroke="#38bdf8" stroke-width="2" opacity="0.6"/> <path d="M 110 260 Q 140 200 170 260" fill="none" stroke="#f59e0b" stroke-width="2" opacity="0.6"/> <circle cx="100" cy="230" r="3" fill="#38bdf8"/> <circle cx="140" cy="230" r="3" fill="#f59e0b"/> <text x="190" y="210" font-family="sans-serif" font-size="13" fill="#f8fafc" width="200"> <tspan x="190" dy="0">• Subjects in Group A provide no</tspan> <tspan x="190" dy="18"> info about Group B.</tspan> <tspan x="190" dy="18">• Default: Welch's T-Test</tspan> <tspan x="190" dy="18">• Handles unequal variances.</tspan> </text> <!-- Card 2: Paired Samples --> <rect x="460" y="120" width="400" height="180" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="485" y="150" font-family="sans-serif" font-weight="700" font-size="18" fill="#e879f9">Paired / Matched T-Test</text> <text x="485" y="172" font-family="sans-serif" font-size="12" fill="#94a3b8">RELATED SUBJECTS / REPEATED MEASURES</text> <!-- Icon: Before/After --> <circle cx="510" cy="235" r="12" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="510" y="239" text-anchor="middle" font-family="sans-serif" font-size="8" fill="#e879f9">T1</text> <path d="M 525 235 L 555 235" stroke="#94a3b8" stroke-dasharray="4" marker-end="url(#arrow)"/> <circle cx="570" cy="235" r="12" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="570" y="239" text-anchor="middle" font-family="sans-serif" font-size="8" fill="#e879f9">T2</text> <text x="610" y="210" font-family="sans-serif" font-size="13" fill="#f8fafc"> <tspan x="610" dy="0">• Same subjects tested twice.</tspan> <tspan x="610" dy="18">• Focuses on the "Mean of</tspan> <tspan x="610" dy="18"> Differences" (μd).</tspan> <tspan x="610" dy="18">• Reduces stochastic noise.</tspan> </text> <!-- Card 3: The Welch Formula (Bottom Left) --> <rect x="40" y="320" width="400" height="200" rx="16" fill="#00000020" stroke="#38bdf840"/> <text x="65" y="350" font-family="sans-serif" font-weight="700" font-size="16" fill="#f8fafc">The Aspin-Welch Statistic</text> <!-- Formula Visual --> <g transform="translate(100, 380)"> <text x="70" y="20" text-anchor="middle" font-family="serif" font-size="22" fill="#f8fafc">t =</text> <text x="160" y="5" text-anchor="middle" font-family="serif" font-size="18" fill="#f8fafc">(x₁ - x₂) - (μ₁ - μ₂)</text> <line x1="100" y1="12" x2="220" y2="12" stroke="#f8fafc" stroke-width="1.5"/> <text x="160" y="35" text-anchor="middle" font-family="serif" font-size="20" fill="#f8fafc">√</text> <line x1="168" y1="22" x2="215" y2="22" stroke="#f8fafc" stroke-width="1"/> <text x="185" y="42" text-anchor="middle" font-family="serif" font-size="14" fill="#f8fafc">s₁²/n₁ + s₂²/n₂</text> </g> <text x="65" y="475" font-family="sans-serif" font-size="11" fill="#94a3b8" line-height="1.4"> <tspan x="65" dy="0">Degrees of Freedom (df) are adjusted via the</tspan> <tspan x="65" dy="15">Welch-Satterthwaite equation to account for</tspan> <tspan x="65" dy="15">heteroscedasticity (unequal variances).</tspan> </text> <!-- Card 4: Decision Taxonomy (Bottom Right) --> <rect x="460" y="320" width="400" height="200" rx="16" fill="#ffffff05" stroke="#ffffff10"/> <text x="485" y="350" font-family="sans-serif" font-weight="700" font-size="16" fill="#f59e0b">Test Selection Logic</text> <!-- Mini Decision Tree --> <g transform="translate(485, 375)"> <rect x="0" y="0" width="80" height="25" rx="4" fill="#38bdf820" stroke="#38bdf8"/> <text x="40" y="17" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f8fafc">Data Type?</text> <line x1="40" y1="25" x2="40" y2="45" stroke="#94a3b8"/> <text x="100" y="55" font-family="sans-serif" font-size="10" fill="#94a3b8">Continuous (Means)</text> <text x="-30" y="55" font-family="sans-serif" font-size="10" fill="#94a3b8">Categorical (%)</text> <path d="M 40 45 L 10 70 M 40 45 L 70 70" fill="none" stroke="#94a3b8"/> <rect x="-30" y="70" width="80" height="25" rx="4" fill="#ffffff10" stroke="#ffffff30"/> <text x="10" y="87" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f8fafc">2-Prop Z-Test</text> <rect x="70" y="70" width="80" height="25" rx="4" fill="#ffffff10" stroke="#ffffff30"/> <text x="110" y="87" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#f8fafc">T-Test</text> <line x1="110" y1="95" x2="110" y2="110" stroke="#94a3b8"/> <text x="115" y="125" font-family="sans-serif" font-size="10" fill="#94a3b8">Independent?</text> <path d="M 110 110 L 80 135 M 110 110 L 140 135" fill="none" stroke="#94a3b8"/> <text x="70" y="150" font-family="sans-serif" font-size="9" fill="#38bdf8">YES: Welch</text> <text x="135" y="150" font-family="sans-serif" font-size="9" fill="#e879f9">NO: Paired</text> </g> <!-- Footer / Status Bar --> <rect x="0" y="535" width="900" height="25" fill="#00000040"/> <text x="20" y="552" font-family="sans-serif" font-size="10" fill="#64748b" font-weight="bold">STATISTICAL INFERENCE SERIES</text> <text x="880" y="552" text-anchor="end" font-family="sans-serif" font-size="10" fill="#64748b">MODULE 04: COMPARATIVE ANALYSIS</text> <!-- Accent dots --> <circle cx="40" cy="40" r="4" fill="#f59e0b" filter="glow"/> <circle cx="60" cy="40" r="4" fill="#38bdf8" filter="glow"/> <circle cx="80" cy="40" r="4" fill="#e879f9" filter="glow"/> </svg>Hypothesis Testing with Two Samples image 1Hypothesis Testing with Two Samples - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/hypothesis-testing-two-samples/svg/1Hypothesis Testing with Two Samples diagram 1Hypothesis Testing with Two Samples - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/hypothesis-testing-two-samples/svg/2Hypothesis Testing with Two Samples diagram 2Hypothesis Testing with Two Samples - Introductory Statistics - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <!-- Background and Definitions --> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Base Layers --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="450" y="60" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">THE CHI-SQUARE DISTRIBUTION</text> <text x="450" y="85" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">The Backbone of Categorical Analysis &amp; Variance Testing</text> <line x1="350" y1="105" x2="550" y2="105" stroke="#38bdf8" stroke-width="2" stroke-linecap="round" opacity="0.6"/> <!-- Panel 1: The Foundation --> <rect x="40" y="130" width="260" height="380" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <circle cx="70" cy="160" r="12" fill="#38bdf8"/> <text x="90" y="165" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">FOUNDATIONS</text> <!-- Foundation Visual: Z to Chi-Sq --> <g transform="translate(60, 200)"> <rect width="220" height="80" rx="8" fill="#ffffff05" stroke="#ffffff10"/> <text x="110" y="30" text-anchor="middle" font-family="serif" font-size="16" fill="#f59e0b" font-style="italic">Z ~ N(0, 1)</text> <path d="M 110 40 L 110 55" stroke="#94a3b8" stroke-width="2" marker-end="url(#arrow)"/> <text x="110" y="70" text-anchor="middle" font-family="serif" font-size="18" font-weight="bold" fill="#f8fafc">X = Σ Z²</text> </g> <text x="60" y="310" font-family="sans-serif" font-size="13" fill="#cbd5e1"> <tspan x="60" dy="1.4em">The distribution is formed by</tspan> <tspan x="60" dy="1.4em">summing the squares of</tspan> <tspan x="60" dy="1.4em" fill="#38bdf8" font-weight="bold">k independent standard</tspan> <tspan x="60" dy="1.4em" fill="#38bdf8" font-weight="bold">normal variables.</tspan> </text> <rect x="60" y="410" width="220" height="70" rx="8" fill="#38bdf815" stroke="#38bdf830"/> <text x="75" y="435" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">PARAMETER:</text> <text x="75" y="455" font-family="sans-serif" font-size="16" font-weight="bold" fill="#f8fafc">Degrees of Freedom (k)</text> <!-- Panel 2: The Curves (Evolution) --> <rect x="320" y="130" width="260" height="380" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <circle cx="350" cy="160" r="12" fill="#e879f9"/> <text x="370" y="165" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">THE EVOLUTION</text> <!-- Mini Graph --> <g transform="translate(340, 200)"> <!-- Axes --> <path d="M 0 120 L 220 120 M 0 120 L 0 0" stroke="#94a3b8" stroke-width="1.5" stroke-linecap="round"/> <!-- df=2 (Exponential) --> <path d="M 2 5 C 10 60, 40 110, 200 118" fill="none" stroke="#f59e0b" stroke-width="2" stroke-dasharray="2 1"/> <text x="15" y="40" font-family="sans-serif" font-size="10" fill="#f59e0b">df=2</text> <!-- df=4 (Skewed) --> <path d="M 2 118 C 20 20, 80 40, 200 115" fill="none" stroke="#e879f9" stroke-width="2.5"/> <text x="60" y="50" font-family="sans-serif" font-size="10" fill="#e879f9">df=4</text> <!-- df=10 (Approaching Normal) --> <path d="M 2 119 C 100 119, 120 60, 150 60 C 180 60, 200 119, 215 119" fill="none" stroke="#38bdf8" stroke-width="2"/> <text x="160" y="55" font-family="sans-serif" font-size="10" fill="#38bdf8">df=10</text> </g> <text x="340" y="350" font-family="sans-serif" font-size="13" fill="#cbd5e1"> <tspan x="340" dy="1.4em">As </tspan> <tspan fill="#e879f9" font-weight="bold">df</tspan> <tspan> increases, the curve shifts</tspan> <tspan x="340" dy="1.4em">right and becomes more</tspan> <tspan x="340" dy="1.4em">symmetrical, eventually</tspan> <tspan x="340" dy="1.4em">mimicking a </tspan> <tspan fill="#38bdf8" font-weight="bold">Normal Curve.</tspan> </text> <!-- Panel 3: Applications --> <rect x="600" y="130" width="260" height="380" rx="16" fill="#ffffff0a" stroke="#ffffff15" stroke-width="1"/> <circle cx="630" cy="160" r="12" fill="#f59e0b"/> <text x="650" y="165" font-family="sans-serif" font-weight="700" font-size="18" fill="#f8fafc">APPLICATIONS</text> <!-- Application 1: Goodness of Fit --> <g transform="translate(620, 190)"> <rect width="220" height="60" rx="8" fill="#f59e0b10" stroke="#f59e0b30"/> <text x="10" y="20" font-family="sans-serif" font-size="12" font-weight="bold" fill="#f59e0b">GOODNESS OF FIT</text> <text x="10" y="40" font-family="sans-serif" font-size="11" fill="#94a3b8">Does data match a model?</text> <!-- Mini Bar Chart Icon --> <rect x="160" y="15" width="8" height="30" fill="#f59e0b" opacity="0.8"/> <rect x="172" y="25" width="8" height="20" fill="#f59e0b" opacity="0.4"/> <rect x="184" y="10" width="8" height="35" fill="#f59e0b" opacity="0.8"/> </g> <!-- Application 2: Independence --> <g transform="translate(620, 265)"> <rect width="220" height="60" rx="8" fill="#38bdf810" stroke="#38bdf830"/> <text x="10" y="20" font-family="sans-serif" font-size="12" font-weight="bold" fill="#38bdf8">INDEPENDENCE TEST</text> <text x="10" y="40" font-family="sans-serif" font-size="11" fill="#94a3b8">Are two variables related?</text> <!-- Table Icon --> <rect x="160" y="15" width="30" height="30" rx="2" fill="none" stroke="#38bdf8" stroke-width="1"/> <line x1="160" y1="25" x2="190" y2="25" stroke="#38bdf8" stroke-width="1"/> <line x1="175" y1="15" x2="175" y2="45" stroke="#38bdf8" stroke-width="1"/> </g> <!-- Formula Section --> <rect x="620" y="345" width="220" height="135" rx="8" fill="#00000020" stroke="#ffffff10"/> <text x="730" y="370" text-anchor="middle" font-family="sans-serif" font-size="12" font-weight="bold" fill="#94a3b8">CORE STATISTIC</text> <text x="730" y="415" text-anchor="middle" font-family="serif" font-size="24" font-weight="bold" fill="#f8fafc" filter="url(#glow)"> χ² = Σ <tspan font-size="16" dy="-10">(O - E)²</tspan><tspan font-size="24" dx="-45" dy="10">———</tspan><tspan font-size="16" dx="-40" dy="12">E</tspan> </text> <text x="730" y="460" text-anchor="middle" font-family="sans-serif" font-size="10" fill="#94a3b8">O = Observed | E = Expected</text> <!-- Footer Properties --> <g transform="translate(40, 525)"> <text x="0" y="0" font-family="sans-serif" font-size="11" font-weight="bold" fill="#38bdf8">SUPPORT: <tspan fill="#f8fafc" font-weight="normal">[0, ∞)</tspan></text> <text x="150" y="0" font-family="sans-serif" font-size="11" font-weight="bold" fill="#e879f9">MEAN: <tspan fill="#f8fafc" font-weight="normal">k</tspan></text> <text x="280" y="0" font-family="sans-serif" font-size="11" font-weight="bold" fill="#f59e0b">VARIANCE: <tspan fill="#f8fafc" font-weight="normal">2k</tspan></text> <text x="450" y="0" font-family="sans-serif" font-size="11" font-weight="bold" fill="#94a3b8">SKEWNESS: <tspan fill="#f8fafc" font-weight="normal">√(8/k)</tspan></text> </g> <!-- Decorative Elements --> <circle cx="850" cy="50" r="30" fill="#e879f9" opacity="0.05"/> <circle cx="50" cy="510" r="40" fill="#38bdf8" opacity="0.05"/> </svg>The Chi-Square Distribution image 1The Chi-Square Distribution - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/the-chi-square-distribution/svg/1The Chi-Square Distribution diagram 1The Chi-Square Distribution - Introductory Statistics - diagram 1<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="0"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2.5" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> <pattern id="dots" x="0" y="0" width="20" height="20" patternUnits="userSpaceOnUse"> <circle cx="2" cy="2" r="1" fill="#ffffff10" /> </pattern> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#dots)"/> <!-- Header --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">LINEAR REGRESSION &amp; CORRELATION</text> <text x="40" y="85" font-family="sans-serif" font-size="16" fill="#94a3b8" letter-spacing="1">STATISTICAL MODELING &amp; PREDICTIVE ANALYTICS</text> <rect x="40" y="100" width="120" height="4" fill="url(#accentGrad)" rx="2"/> <!-- Main Visualization Card --> <rect x="40" y="130" width="520" height="320" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <!-- Grid Lines for Plot --> <g stroke="#94a3b830" stroke-width="1" stroke-dasharray="4 4"> <line x1="80" y1="170" x2="520" y2="170"/> <line x1="80" y1="230" x2="520" y2="230"/> <line x1="80" y1="290" x2="520" y2="290"/> <line x1="80" y1="350" x2="520" y2="350"/> <line x1="80" y1="410" x2="520" y2="410"/> </g> <!-- Axes --> <line x1="80" y1="160" x2="80" y2="410" stroke="#94a3b8" stroke-width="2"/> <line x1="80" y1="410" x2="530" y2="410" stroke="#94a3b8" stroke-width="2"/> <text x="535" y="425" font-family="sans-serif" font-size="12" fill="#94a3b8" font-weight="bold">X (Predictor)</text> <text x="60" y="150" font-family="sans-serif" font-size="12" fill="#94a3b8" font-weight="bold">Y (Outcome)</text> <!-- Residuals (Vertical Lines) --> <g stroke="#f59e0b" stroke-width="1.5" stroke-dasharray="2 2" opacity="0.6"> <line x1="120" y1="380" x2="120" y2="385"/> <line x1="180" y1="330" x2="180" y2="345"/> <line x1="240" y1="350" x2="240" y2="305"/> <line x1="300" y1="250" x2="300" y2="265"/> <line x1="360" y1="210" x2="360" y2="225"/> <line x1="420" y1="230" x2="420" y2="185"/> <line x1="480" y1="140" x2="480" y2="145"/> </g> <!-- Data Points --> <g fill="#38bdf8"> <circle cx="120" cy="380" r="5" filter="glow"/> <circle cx="180" cy="330" r="5" filter="glow"/> <circle cx="240" cy="350" r="5" filter="glow"/> <circle cx="300" cy="250" r="5" filter="glow"/> <circle cx="360" cy="210" r="5" filter="glow"/> <circle cx="420" cy="230" r="5" filter="glow"/> <circle cx="480" cy="140" r="5" filter="glow"/> </g> <!-- Regression Line --> <line x1="80" y1="412" x2="520" y2="118" stroke="#e879f9" stroke-width="4" filter="glow"/> <!-- Callout: Residuals --> <path d="M 420 205 L 450 180" stroke="#f59e0b" fill="none" stroke-width="1"/> <text x="455" y="175" font-family="sans-serif" font-size="11" fill="#f59e0b" font-weight="bold">Residual (Error)</text> <text x="455" y="188" font-family="sans-serif" font-size="10" fill="#94a3b8">y - ŷ</text> <!-- Right Panel: Correlation Coefficient --> <rect x="580" y="130" width="280" height="150" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <circle cx="615" cy="165" r="15" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <text x="610" y="170" font-family="sans-serif" font-size="14" fill="#38bdf8" font-weight="bold">r</text> <text x="645" y="160" font-family="sans-serif" font-size="16" fill="#f8fafc" font-weight="bold">Correlation Coefficient</text> <text x="645" y="178" font-family="sans-serif" font-size="12" fill="#94a3b8">Measures Strength &amp; Direction</text> <rect x="600" y="205" width="240" height="8" rx="4" fill="#0f172a"/> <rect x="720" y="205" width="80" height="8" rx="4" fill="url(#accentGrad)"/> <text x="600" y="235" font-family="sans-serif" font-size="11" fill="#94a3b8">-1.0</text> <text x="715" y="235" font-family="sans-serif" font-size="11" fill="#f8fafc">0</text> <text x="820" y="235" font-family="sans-serif" font-size="11" fill="#94a3b8">+1.0</text> <text x="600" y="260" font-family="sans-serif" font-size="12" fill="#e879f9" font-style="italic">"How tight is the cloud?"</text> <!-- Right Panel: Regression Equation --> <rect x="580" y="300" width="280" height="150" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <path d="M 605 345 L 625 325 M 605 325 L 625 345" stroke="#e879f9" stroke-width="3" opacity="0.8"/> <text x="645" y="330" font-family="sans-serif" font-size="16" fill="#f8fafc" font-weight="bold">Least-Squares Line</text> <text x="645" y="348" font-family="sans-serif" font-size="12" fill="#94a3b8">The Predictive Model</text> <text x="605" y="395" font-family="serif" font-size="28" fill="#f8fafc">ŷ = a + bx</text> <text x="605" y="425" font-family="sans-serif" font-size="11" fill="#94a3b8">a = Intercept | b = Slope</text> <!-- Bottom: Coefficient of Determination --> <rect x="40" y="470" width="820" height="60" rx="16" fill="#ffffff05" stroke="#ffffff10"/> <text x="70" y="505" font-family="sans-serif" font-size="18" fill="#f59e0b" font-weight="bold">r²</text> <text x="100" y="505" font-family="sans-serif" font-size="16" fill="#f8fafc" font-weight="bold">Coefficient of Determination:</text> <text x="340" y="505" font-family="sans-serif" font-size="14" fill="#94a3b8">The proportion of variance in Y explained by the linear relationship with X.</text> <!-- Decorative Math Symbols --> <text x="800" y="80" font-family="serif" font-size="40" fill="#ffffff05" transform="rotate(15)">Σ</text> <text x="840" y="500" font-family="serif" font-size="30" fill="#ffffff05" transform="rotate(-10)">μ</text> <text x="50" y="530" font-family="serif" font-size="24" fill="#ffffff05">σ</text> </svg>Linear Regression and Correlation image 1Linear Regression and Correlation - Introductory Statistics - image 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/linear-regression-and-correlation/svg/1Linear Regression and Correlation diagram 1Linear Regression and Correlation - Introductory Statistics - diagram 1https://www.getlykke.com/explore/public/introductory-statistics-a4146afb-5db4-4b78-bb6a-8cef9d5ce9e0/media/linear-regression-and-correlation/svg/2Linear Regression and Correlation diagram 2Linear Regression and Correlation - Introductory Statistics - diagram 2https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb0518612026-04-20T04:36:19.000Z<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="slinky-grad" x1="0%" y1="0%" x2="100%" y2="0%"> <stop offset="0%" stop-color="#f59e0b"/> <stop offset="33%" stop-color="#38bdf8"/> <stop offset="66%" stop-color="#e879f9"/> <stop offset="100%" stop-color="#10b981"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header Section --> <text x="40" y="50" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">THE WRITING PROCESS</text> <text x="40" y="75" font-family="sans-serif" font-weight="400" font-size="16" fill="#94a3b8">A Recursive Journey: From Creative Entropy to Surgical Precision</text> <rect x="40" y="90" width="120" height="4" fill="#38bdf8" rx="2"/> <!-- Comparison Panel (Top Right) --> <rect x="560" y="30" width="300" height="110" rx="16" fill="#ffffff10" stroke="#ffffff20"/> <text x="580" y="55" font-family="sans-serif" font-weight="700" font-size="14" fill="#f8fafc">THE PARADIGM SHIFT</text> <text x="580" y="80" font-family="sans-serif" font-size="12" fill="#94a3b8">Linear Model: Static, Unidirectional</text> <path d="M 780 76 L 830 76" stroke="#ef4444" stroke-width="2" marker-end="url(#arrow)"/> <text x="580" y="100" font-family="sans-serif" font-size="12" fill="#38bdf8">Recursive Model: Dynamic, Cyclical</text> <path d="M 780 96 C 790 86, 820 86, 830 96 S 800 106, 790 96" fill="none" stroke="#38bdf8" stroke-width="2"/> <!-- Main Slinky Path (The Core Visual) --> <g transform="translate(50, 180)"> <!-- Shadow/Path Trace --> <path d="M 50 100 C 50 0, 150 0, 150 100 S 250 200, 250 100 S 350 0, 350 100 S 450 200, 450 100 S 550 0, 550 100 S 650 200, 650 100 S 750 0, 750 100" fill="none" stroke="#ffffff10" stroke-width="40" stroke-linecap="round"/> <!-- The Slinky Coil --> <path d="M 50 100 C 50 0, 150 0, 150 100 S 250 200, 250 100 S 350 0, 350 100 S 450 200, 450 100 S 550 0, 550 100 S 650 200, 650 100 S 750 0, 750 100" fill="none" stroke="url(#slinky-grad)" stroke-width="8" stroke-dasharray="1, 15" stroke-linecap="round" filter="url(#glow)"/> <!-- Loop Back Indicators --> <path d="M 250 120 Q 200 160, 150 120" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4" marker-end="url(#arrow-head)"/> <path d="M 450 120 Q 400 160, 350 120" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4" marker-end="url(#arrow-head)"/> <path d="M 650 120 Q 600 160, 550 120" fill="none" stroke="#94a3b8" stroke-width="2" stroke-dasharray="4" marker-end="url(#arrow-head)"/> </g> <!-- Phase Cards --> <!-- 1. Prewriting --> <rect x="40" y="380" width="190" height="140" rx="12" fill="#ffffff08" stroke="#f59e0b44"/> <circle cx="70" cy="410" r="15" fill="#f59e0b22" stroke="#f59e0b" stroke-width="2"/> <path d="M 65 405 L 75 415 M 75 405 L 65 415" stroke="#f59e0b" stroke-width="2"/> <text x="95" y="415" font-family="sans-serif" font-weight="700" font-size="16" fill="#f59e0b">PREWRITING</text> <text x="60" y="445" font-family="sans-serif" font-size="12" fill="#f8fafc">Creative Entropy</text> <text x="60" y="465" font-family="sans-serif" font-size="11" fill="#94a3b8">• Brainstorming</text> <text x="60" y="480" font-family="sans-serif" font-size="11" fill="#94a3b8">• Cluster Mapping</text> <text x="60" y="495" font-family="sans-serif" font-size="11" fill="#94a3b8">• Freewriting</text> <!-- 2. 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Revising --> <rect x="460" y="380" width="190" height="140" rx="12" fill="#ffffff08" stroke="#e879f944"/> <circle cx="490" cy="410" r="15" fill="#e879f922" stroke="#e879f9" stroke-width="2"/> <path d="M 485 410 A 5 5 0 1 1 495 410" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="515" y="415" font-family="sans-serif" font-weight="700" font-size="16" fill="#e879f9">REVISING</text> <text x="480" y="445" font-family="sans-serif" font-size="12" fill="#f8fafc">Refinement</text> <text x="480" y="465" font-family="sans-serif" font-size="11" fill="#94a3b8">• Global Changes</text> <text x="480" y="480" font-family="sans-serif" font-size="11" fill="#94a3b8">• Argument Strength</text> <text x="480" y="495" font-family="sans-serif" font-size="11" fill="#94a3b8">• Structural Reorg</text> <!-- 4. Editing --> <rect x="670" y="380" width="190" height="140" rx="12" fill="#ffffff08" stroke="#10b98144"/> <circle cx="700" cy="410" r="15" fill="#10b98122" stroke="#10b981" stroke-width="2"/> <path d="M 695 415 L 705 405" stroke="#10b981" stroke-width="2"/> <text x="725" y="415" font-family="sans-serif" font-weight="700" font-size="16" fill="#10b981">EDITING</text> <text x="690" y="445" font-family="sans-serif" font-size="12" fill="#f8fafc">Precision</text> <text x="690" y="465" font-family="sans-serif" font-size="11" fill="#94a3b8">• Sentence Flow</text> <text x="690" y="480" font-family="sans-serif" font-size="11" fill="#94a3b8">• Grammar/Syntax</text> <text x="690" y="495" font-family="sans-serif" font-size="11" fill="#94a3b8">• Final Polish</text> <!-- Markers --> <marker id="arrow-head" markerWidth="10" markerHeight="10" refX="5" refY="5" orient="auto"> <path d="M 0 0 L 5 5 L 0 10" fill="none" stroke="#94a3b8" stroke-width="1"/> </marker> <!-- Quote/Principle --> <text x="450" y="545" font-family="sans-serif" font-style="italic" font-size="13" fill="#94a3b8" text-anchor="middle">"Writing is not merely a way to record thoughts, but a way to discover them."</text> <!-- Decorative "Slinky Principle" Label --> <g transform="translate(100, 200) rotate(-15)"> <text x="0" y="0" font-family="sans-serif" font-weight="900" font-size="10" fill="#ffffff20" letter-spacing="2">THE SLINKY PRINCIPLE</text> </g> </svg>The Writing Process Overview image 1The Writing Process Overview - Online Writing Lab - image 1https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb051861/media/the-writing-process-overview/svg/1The Writing Process Overview diagram 1The Writing Process Overview - Online Writing Lab - diagram 1https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb051861/media/the-writing-process-overview/svg/2The Writing Process Overview diagram 2The Writing Process Overview - Online Writing Lab - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <linearGradient id="accentGrad" x1="0" y1="0" x2="1" y2="1"> <stop offset="0%" stop-color="#38bdf8"/> <stop offset="100%" stop-color="#e879f9"/> </linearGradient> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background and Grid --> <rect width="900" height="560" fill="url(#bg)"/> <g stroke="#ffffff08" stroke-width="1"> <path d="M0 40h900M0 80h900M0 120h900M0 160h900M0 200h900M0 240h900M0 280h900M0 320h900M0 360h900M0 400h900M0 440h900M0 480h900M0 520h900"/> <path d="M40 0v560M80 0v560M120 0v560M160 0v560M200 0v560M240 0v560M280 0v560M320 0v560M360 0v560M400 0v560M440 0v560M480 0v560M520 0v560M560 0v560M600 0v560M640 0v560M680 0v560M720 0v560M760 0v560M800 0v560M840 0v560"/> </g> <!-- Header Section --> <text x="40" y="60" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc">PREWRITING &amp; IDEA GENERATION</text> <text x="40" y="85" font-family="sans-serif" font-size="14" fill="#94a3b8" letter-spacing="1">THE NON-LINEAR ARCHITECTURE OF THOUGHT</text> <rect x="40" y="105" width="120" height="4" fill="url(#accentGrad)" rx="2"/> <!-- Main Concept: The Slinky Metaphor --> <rect x="40" y="130" width="410" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="60" y="165" font-family="sans-serif" font-weight="700" font-size="18" fill="#38bdf8">The Recursive Loop (The Slinky®)</text> <text x="60" y="185" font-family="sans-serif" font-size="12" fill="#94a3b8">Writing is not a straight line, but a forward-moving coil.</text> <!-- Slinky Illustration --> <g transform="translate(80, 240)" fill="none" stroke-width="3"> <path d="M0 0c20-40 60-40 80 0s-60 40-80 0" stroke="#38bdf833"/> <path d="M40 0c20-40 60-40 80 0s-60 40-80 0" stroke="#38bdf866"/> <path d="M80 0c20-40 60-40 80 0s-60 40-80 0" stroke="#38bdf899"/> <path d="M120 0c20-40 60-40 80 0s-60 40-80 0" stroke="#38bdf8"/> <path d="M160 0c20-40 60-40 80 0s-60 40-80 0" stroke="#e879f9" filter="url(#glow)"/> <!-- Arrow --> <path d="M250 0h60" stroke="#f8fafc" stroke-dasharray="4 2"/> <path d="M305 -5l10 5l-10 5" fill="#f8fafc"/> </g> <text x="60" y="340" font-family="sans-serif" font-size="12" fill="#f8fafc" font-weight="600">RECURSIVE PROGRESSION</text> <text x="280" y="340" font-family="sans-serif" font-size="11" fill="#94a3b8">Iteration leads to refinement</text> <!-- Comparison: Generative vs Evaluative --> <rect x="470" y="130" width="390" height="240" rx="16" fill="#ffffff0a" stroke="#ffffff15"/> <text x="490" y="165" font-family="sans-serif" font-weight="700" font-size="18" fill="#f59e0b">Cognitive Decoupling</text> <!-- Generative Side --> <rect x="490" y="185" width="170" height="160" rx="8" fill="#38bdf810" stroke="#38bdf830"/> <text x="500" y="205" font-family="sans-serif" font-weight="700" font-size="13" fill="#38bdf8">GENERATIVE</text> <text x="500" y="225" font-family="sans-serif" font-size="11" fill="#f8fafc">Divergent Thinking</text> <circle cx="510" cy="255" r="3" fill="#38bdf8"/> <text x="520" y="259" font-family="sans-serif" font-size="11" fill="#94a3b8">Quantity over quality</text> <circle cx="510" cy="275" r="3" fill="#38bdf8"/> <text x="520" y="279" font-family="sans-serif" font-size="11" fill="#94a3b8">Bypass inner critic</text> <circle cx="510" cy="295" r="3" fill="#38bdf8"/> <text x="520" y="299" font-family="sans-serif" font-size="11" fill="#94a3b8">Raw conceptual ore</text> <!-- Evaluative Side --> <rect x="670" y="185" width="170" height="160" rx="8" fill="#e879f910" stroke="#e879f930"/> <text x="680" y="205" font-family="sans-serif" font-weight="700" font-size="13" fill="#e879f9">EVALUATIVE</text> <text x="680" y="225" font-family="sans-serif" font-size="11" fill="#f8fafc">Convergent Thinking</text> <circle cx="690" cy="255" r="3" fill="#e879f9"/> <text x="700" y="259" font-family="sans-serif" font-size="11" fill="#94a3b8">Clarity and logic</text> <circle cx="690" cy="275" r="3" fill="#e879f9"/> <text x="700" y="279" font-family="sans-serif" font-size="11" fill="#94a3b8">Strict constraints</text> <circle cx="690" cy="295" r="3" fill="#e879f9"/> <text x="700" y="299" font-family="sans-serif" font-size="11" fill="#94a3b8">Polishing the metal</text> <!-- Bottom Section: Methodologies --> <text x="40" y="410" font-family="sans-serif" font-weight="700" font-size="20" fill="#f8fafc">Core Methodologies</text> <!-- Freewriting Card --> <rect x="40" y="430" width="410" height="100" rx="12" fill="#ffffff0a" stroke="#ffffff15"/> <path d="M60 455l20 0l5 15l10-30l10 40l10-25l10 0" stroke="#38bdf8" fill="none" stroke-width="2"/> <text x="140" y="460" font-family="sans-serif" font-weight="700" font-size="16" fill="#f8fafc">01. Freewriting</text> <text x="140" y="480" font-family="sans-serif" font-size="12" fill="#94a3b8">Stochastic generation. Maintain velocity to</text> <text x="140" y="495" font-family="sans-serif" font-size="12" fill="#94a3b8">achieve flow state and lower entry barriers.</text> <rect x="140" y="508" width="60" height="14" rx="4" fill="#38bdf820"/> <text x="145" y="519" font-family="sans-serif" font-size="9" font-weight="bold" fill="#38bdf8">VELOCITY</text> <!-- Mapping Card --> <rect x="470" y="430" width="390" height="100" rx="12" fill="#ffffff0a" stroke="#ffffff15"/> <!-- Node Icon --> <circle cx="510" cy="480" r="6" stroke="#e879f9" stroke-width="2" fill="none"/> <circle cx="535" cy="460" r="4" fill="#e879f9"/> <circle cx="535" cy="500" r="4" fill="#e879f9"/> <line x1="516" y1="476" x2="531" y2="464" stroke="#e879f9" stroke-width="1"/> <line x1="516" y1="484" x2="531" y2="496" stroke="#e879f9" stroke-width="1"/> <text x="560" y="460" font-family="sans-serif" font-weight="700" font-size="16" fill="#f8fafc">02. Concept Mapping</text> <text x="560" y="480" font-family="sans-serif" font-size="12" fill="#94a3b8">Visual synthesis of nodes and edges.</text> <text x="560" y="495" font-family="sans-serif" font-size="12" fill="#94a3b8">Identifies the topology of an argument.</text> <rect x="560" y="508" width="60" height="14" rx="4" fill="#e879f920"/> <text x="565" y="519" font-family="sans-serif" font-size="9" font-weight="bold" fill="#e879f9">STRUCTURE</text> <!-- Decorative corner element --> <path d="M860 40l20 0l0 20" fill="none" stroke="#f59e0b" stroke-width="2"/> <circle cx="880" cy="40" r="3" fill="#f59e0b"/> </svg>Prewriting and Idea Generation image 1Prewriting and Idea Generation - Online Writing Lab - image 1https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb051861/media/prewriting-strategies/svg/1Prewriting and Idea Generation diagram 1Prewriting and Idea Generation - Online Writing Lab - diagram 1https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb051861/media/prewriting-strategies/svg/2Prewriting and Idea Generation diagram 2Prewriting and Idea Generation - Online Writing Lab - diagram 2https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb051861/media/prewriting-strategies/svg/3Prewriting and Idea Generation diagram 3Prewriting and Idea Generation - Online Writing Lab - diagram 3<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="2" result="coloredBlur"/> <feMerge> <feMergeNode in="coloredBlur"/> <feMergeNode in="SourceGraphic"/> </feMerge> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-size="32" font-weight="800" fill="#f8fafc" letter-spacing="1">ASSIGNMENT ANALYSIS &amp; TOPIC NARROWING</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="400" fill="#94a3b8" letter-spacing="2">PHASE 01: THE RHETORICAL COMPILER</text> <line x1="350" y1="85" x2="550" y2="85" stroke="#38bdf8" stroke-width="2" stroke-dasharray="4 2"/> <!-- Left Section: Rhetorical Triad --> <text x="60" y="125" font-family="sans-serif" font-size="18" font-weight="700" fill="#38bdf8">I. THE RHETORICAL TRIAD</text> <!-- Purpose Card --> <rect x="50" y="140" width="320" height="85" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <circle cx="85" cy="182" r="20" fill="#38bdf820" stroke="#38bdf8" stroke-width="2"/> <circle cx="85" cy="182" r="4" fill="#38bdf8"/> <text x="120" y="175" font-family="sans-serif" font-size="16" font-weight="700" fill="#f8fafc">PURPOSE</text> <text x="120" y="192" font-family="sans-serif" font-size="12" fill="#94a3b8">The "Why" — Objective Function (Persuade/Inform)</text> <!-- Audience Card --> <rect x="50" y="240" width="320" height="85" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <path d="M75 285 Q85 265 95 285" fill="none" stroke="#f59e0b" stroke-width="2"/> <circle cx="85" cy="270" r="6" fill="none" stroke="#f59e0b" stroke-width="2"/> <text x="120" y="275" font-family="sans-serif" font-size="16" font-weight="700" fill="#f8fafc">AUDIENCE</text> <text x="120" y="292" font-family="sans-serif" font-size="12" fill="#94a3b8">The "Who" — Knowledge Threshold &amp; Abstraction</text> <!-- Voice Card --> <rect x="50" y="340" width="320" height="85" rx="16" fill="#ffffff10" stroke="#ffffff15"/> <path d="M70 382 L75 372 L85 392 L90 382 L100 382" fill="none" stroke="#e879f9" stroke-width="2"/> <text x="120" y="375" font-family="sans-serif" font-size="16" font-weight="700" fill="#f8fafc">VOICE</text> <text x="120" y="392" font-family="sans-serif" font-size="12" fill="#94a3b8">The "How" — Register, Tone, &amp; Ethos</text> <!-- Right Section: The Hand Fan / Funnel --> <text x="500" y="125" font-family="sans-serif" font-size="18" font-weight="700" fill="#f59e0b">II. TOPIC NARROWING (THE FAN)</text> <!-- Funnel/Fan Visualization --> <g transform="translate(500, 150)"> <!-- Level 1: Global --> <path d="M0 0 L340 0 L310 60 L30 60 Z" fill="#ffffff08" stroke="#ffffff20"/> <text x="170" y="35" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">GLOBAL TOPIC (Too Broad)</text> <text x="350" y="35" font-family="sans-serif" font-size="11" fill="#94a3b8">e.g., "Climate Change"</text> <!-- Level 2: Category --> <path d="M30 70 L310 70 L270 130 L70 130 Z" fill="#ffffff12" stroke="#ffffff20"/> <text x="170" y="105" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">SUB-CATEGORY</text> <text x="350" y="105" font-family="sans-serif" font-size="11" fill="#94a3b8">e.g., "Ocean Acidification"</text> <!-- Level 3: Niche --> <path d="M70 140 L270 140 L220 200 L120 200 Z" fill="#38bdf820" stroke="#38bdf840"/> <text x="170" y="175" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="700" fill="#f8fafc">SPECIFIC NICHE</text> <text x="350" y="175" font-family="sans-serif" font-size="11" fill="#94a3b8">e.g., "Impact on Coral Reefs"</text> <!-- Level 4: Thesis --> <path d="M120 210 L220 210 L170 270 Z" fill="#f59e0b40" stroke="#f59e0b" filter="url(#glow)"/> <text x="170" y="245" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="800" fill="#f59e0b">THESIS RIB</text> <text x="180" y="295" font-family="sans-serif" font-size="11" fill="#f8fafc" font-style="italic">"The economic impact of coral bleaching on Caribbean tourism (2010-2020)"</text> </g> <!-- Bottom Panel: Logic Check --> <rect x="50" y="450" width="800" height="80" rx="16" fill="#00000040" stroke="#38bdf830"/> <text x="75" y="475" font-family="monospace" font-size="13" fill="#38bdf8">if capacity &lt; 0.8: </text> <text x="215" y="475" font-family="monospace" font-size="13" fill="#f8fafc">return "REJECT: Scope Creep Detected"</text> <text x="75" y="495" font-family="monospace" font-size="13" fill="#38bdf8">elif capacity &gt; 2.5: </text> <text x="235" y="495" font-family="monospace" font-size="13" fill="#f8fafc">return "CAUTION: Topic too thin"</text> <!-- Success Metric Badge --> <rect x="680" y="465" width="150" height="50" rx="10" fill="#10b98120" stroke="#10b981"/> <text x="755" y="485" text-anchor="middle" font-family="sans-serif" font-size="10" font-weight="700" fill="#10b981">SUCCESS METRIC</text> <text x="755" y="502" text-anchor="middle" font-family="sans-serif" font-size="14" font-weight="800" fill="#f8fafc">OPTIMAL ALIGNMENT</text> <!-- Decorative elements --> <circle cx="850" cy="50" r="30" fill="none" stroke="#ffffff05" stroke-width="8"/> <circle cx="850" cy="50" r="15" fill="none" stroke="#ffffff05" stroke-width="4"/> </svg>Assignment Analysis and Topic Narrowing image 1Assignment Analysis and Topic Narrowing - Online Writing Lab - image 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stroke="#38bdf815" stroke-width="1"/> <circle cx="450" cy="280" r="220" fill="none" stroke="#e879f910" stroke-width="1"/> <!-- Left Card: The Rhetorical Situation (Input) --> <rect x="50" y="140" width="220" height="280" rx="16" fill="#ffffff08" stroke="#ffffff15" stroke-width="1"/> <text x="70" y="175" fill="#38bdf8" font-family="sans-serif" font-size="18" font-weight="700">Rhetorical Situation</text> <g transform="translate(70, 205)"> <circle cx="10" cy="0" r="4" fill="#f59e0b"/> <text x="25" y="5" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="600">Exigence</text> <text x="25" y="22" fill="#94a3b8" font-family="sans-serif" font-size="11">The catalyst for writing</text> <circle cx="10" cy="50" r="4" fill="#f59e0b"/> <text x="25" y="55" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="600">Constraints</text> <text x="25" y="72" fill="#94a3b8" font-family="sans-serif" font-size="11">Rubrics, medium, rules</text> <circle cx="10" cy="100" r="4" fill="#f59e0b"/> <text x="25" y="105" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="600">The Signal</text> <text x="25" y="122" fill="#94a3b8" font-family="sans-serif" font-size="11">Writer-based prose</text> </g> <!-- Center: The Academic Voice Filter --> <rect x="320" y="120" width="260" height="320" rx="20" fill="#ffffff10" stroke="#38bdf840" stroke-width="2"/> <rect x="320" y="120" width="260" height="50" rx="20" fill="#38bdf820"/> <text x="450" y="152" text-anchor="middle" fill="#f8fafc" font-family="sans-serif" font-size="18" font-weight="800">ACADEMIC VOICE</text> <!-- Protocol Components --> <g transform="translate(345, 200)"> <rect width="210" height="60" rx="8" fill="#0f172a60" stroke="#ffffff10"/> <text x="15" y="25" fill="#e879f9" font-family="sans-serif" font-size="13" font-weight="700">OBJECTIVITY</text> <text x="15" y="45" fill="#94a3b8" font-family="sans-serif" font-size="11">Minimize Subjective Bias (S)</text> <rect y="75" width="210" height="60" 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font-family="sans-serif" font-size="14" font-weight="600">Intelligent Non-Expert</text> <text x="0" y="42" fill="#94a3b8" font-family="sans-serif" font-size="11">High logic, low domain context</text> <text x="0" y="85" fill="#f8fafc" font-family="sans-serif" font-size="14" font-weight="600">Reader-Based Prose</text> <text x="0" y="102" fill="#94a3b8" font-family="sans-serif" font-size="11">Optimized for cognitive load</text> <!-- Target Icon --> <circle cx="90" cy="160" r="30" fill="none" stroke="#e879f930" stroke-width="2"/> <circle cx="90" cy="160" r="20" fill="none" stroke="#e879f960" stroke-width="2"/> <circle cx="90" cy="160" r="5" fill="#e879f9" filter="url(#glow)"/> </g> <!-- Bottom: Mathematical Representation --> <rect x="250" y="470" width="400" height="60" rx="30" fill="#0f172a" stroke="url(#accentGrad)" stroke-width="1.5"/> <text x="450" y="505" text-anchor="middle" fill="#f8fafc" font-family="monospace" font-size="22"> E = <tspan fill="#38bdf8">C</tspan> · <tspan fill="#38bdf8">A</tspan> / (<tspan fill="#e879f9">S</tspan> + 1) </text> <text x="450" y="522" text-anchor="middle" fill="#94a3b8" font-family="sans-serif" font-size="10" letter-spacing="0.1em">EFFECTIVENESS = (CLARITY × AUTHORITY) / (SUBJECTIVITY + 1)</text> <!-- Connecting Arrows --> <path d="M 270 280 L 310 280" stroke="#38bdf8" stroke-width="2" fill="none" marker-end="url(#arrow)"/> <path d="M 580 280 L 620 280" stroke="#e879f9" stroke-width="2" fill="none" marker-end="url(#arrow)"/> <defs> <marker id="arrow" markerWidth="10" markerHeight="10" refX="9" refY="5" orientation="auto"> <path d="M0,0 L10,5 L0,10 Z" fill="#38bdf8" /> </marker> </defs> <!-- Decorative Corner Elements --> <circle cx="30" cy="30" r="20" fill="#38bdf810"/> <circle cx="870" cy="530" r="40" fill="#e879f905"/> <path d="M 850 30 L 880 30 M 865 15 L 865 45" stroke="#ffffff20" stroke-width="2"/> </svg>Audience Awareness and Academic Voice image 1Audience Awareness and Academic Voice - Online Writing Lab - image 1https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb051861/media/audience-and-voice/svg/1Audience Awareness and Academic Voice diagram 1Audience Awareness and Academic Voice - Online Writing Lab - diagram 1https://www.getlykke.com/explore/public/online-writing-lab-5f0d98fb-87e2-439f-abc2-dde0bb051861/media/audience-and-voice/svg/2Audience Awareness and Academic Voice diagram 2Audience Awareness and Academic Voice - Online Writing Lab - diagram 2<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 900 560"> <defs> <linearGradient id="bg" x1="0" y1="0" x2="0" y2="1"> <stop offset="0%" stop-color="#0f172a"/> <stop offset="100%" stop-color="#1e1b4b"/> </linearGradient> <pattern id="grid" width="40" height="40" patternUnits="userSpaceOnUse"> <path d="M 40 0 L 0 0 0 40" fill="none" stroke="#ffffff08" stroke-width="1"/> </pattern> <filter id="glow"> <feGaussianBlur stdDeviation="3" result="blur"/> <feComposite in="SourceGraphic" in2="blur" operator="over"/> </filter> </defs> <!-- Background --> <rect width="900" height="560" fill="url(#bg)"/> <rect width="900" height="560" fill="url(#grid)"/> <!-- Decorative Slinky Path (The Recursive Loop) --> <path d="M 50 280 Q 100 100 150 280 T 250 280 T 350 280 T 450 280 T 550 280 T 650 280 T 750 280 T 850 280" fill="none" stroke="#38bdf822" stroke-width="60" stroke-linecap="round"/> <path d="M 50 280 C 80 150, 120 150, 150 280 S 220 410, 250 280 S 320 150, 350 280 S 420 410, 450 280 S 520 150, 550 280 S 620 410, 650 280 S 720 150, 750 280 S 820 410, 850 280" fill="none" stroke="#38bdf844" stroke-width="2" stroke-dasharray="8 4"/> <!-- Header --> <text x="450" y="50" text-anchor="middle" font-family="sans-serif" font-weight="800" font-size="32" fill="#f8fafc" letter-spacing="1">THE ARCHITECTURE OF COMPOSITION</text> <text x="450" y="75" text-anchor="middle" font-family="sans-serif" font-size="14" fill="#94a3b8" font-style="italic">Writing as a Recursive, Non-Linear Cognitive Process</text> <!-- Section 1: Pre-Drafting (The Pivot) --> <rect x="40" y="110" width="200" height="160" rx="16" fill="#ffffff10" stroke="#38bdf8" stroke-width="1"/> <circle cx="140" cy="145" r="20" fill="#38bdf822" stroke="#38bdf8" stroke-width="2"/> <!-- Hand Fan Icon --> <path d="M 140 155 L 125 135 M 140 155 L 140 130 M 140 155 L 155 135" stroke="#38bdf8" stroke-width="2" fill="none"/> <text x="140" y="185" text-anchor="middle" font-family="sans-serif" font-weight="bold" font-size="16" fill="#f8fafc">1. THE PIVOT POINT</text> <text x="55" y="210" font-family="sans-serif" font-size="12" fill="#94a3b8"> <tspan x="55" dy="0">Narrowing the scope from</tspan> <tspan x="55" dy="16">broad subject to specific</tspan> <tspan x="55" dy="16">researchable inquiry.</tspan> </text> <text x="140" y="255" text-anchor="middle" font-family="sans-serif" font-size="11" font-weight="bold" fill="#38bdf8">TOPIC FEASIBILITY</text> <!-- Section 2: Drafting (The Blueprint) --> <rect x="255" y="320" width="200" height="160" rx="16" fill="#ffffff10" stroke="#f59e0b" stroke-width="1"/> <circle cx="355" cy="355" r="20" fill="#f59e0b22" stroke="#f59e0b" stroke-width="2"/> <!-- DAG Icon --> <circle cx="355" cy="345" r="3" fill="#f59e0b"/> <circle cx="345" cy="365" r="3" fill="#f59e0b"/> <circle cx="365" cy="365" r="3" fill="#f59e0b"/> <path d="M 355 348 L 348 362 M 355 348 L 362 362" stroke="#f59e0b" stroke-width="1.5"/> <text x="355" y="395" text-anchor="middle" font-family="sans-serif" font-weight="bold" font-size="16" fill="#f8fafc">2. THE BLUEPRINT</text> <text x="270" y="420" font-family="sans-serif" font-size="12" fill="#94a3b8"> <tspan x="270" dy="0">Algorithmic structuring.</tspan> <tspan x="270" dy="16">Ensuring every claim acts</tspan> <tspan x="270" dy="16">as a pillar for the thesis.</tspan> </text> <text x="355" y="465" text-anchor="middle" font-family="sans-serif" font-size="11" font-weight="bold" fill="#f59e0b">LOGICAL FLOW (DAG)</text> <!-- Section 3: Revising (Macro) --> <rect x="470" y="110" width="200" height="160" rx="16" fill="#ffffff10" stroke="#e879f9" stroke-width="1"/> <circle cx="570" cy="145" r="20" fill="#e879f922" stroke="#e879f9" stroke-width="2"/> <!-- Macro Icon --> <rect x="560" y="135" width="20" height="20" stroke="#e879f9" fill="none" stroke-width="2"/> <path d="M 560 145 L 580 145 M 570 135 L 570 155" stroke="#e879f9" stroke-width="1"/> <text x="570" y="185" text-anchor="middle" font-family="sans-serif" font-weight="bold" font-size="16" fill="#f8fafc">3. REVISING</text> <text x="485" y="210" font-family="sans-serif" font-size="12" fill="#94a3b8"> <tspan x="485" dy="0">Global adjustments to</tspan> <tspan x="485" dy="16">argument, organization,</tspan> <tspan x="485" dy="16">and evidence strength.</tspan> </text> <text x="570" y="255" text-anchor="middle" font-family="sans-serif" font-size="11" font-weight="bold" fill="#e879f9">MACRO-STRUCTURE</text> <!-- Section 4: Editing (Micro) --> <rect x="685" y="320" width="200" height="160" rx="16" fill="#ffffff10" stroke="#2dd4bf" stroke-width="1"/> <circle cx="785" cy="355" r="20" fill="#2dd4bf22" stroke="#2dd4bf" stroke-width="2"/> <!-- Pen Icon --> <path d="M 778 365 L 792 345" stroke="#2dd4bf" stroke-width="3" stroke-linecap="round"/> <text x="785" y="395" text-anchor="middle" font-family="sans-serif" font-weight="bold" font-size="16" fill="#f8fafc">4. 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