#!/usr/bin/env node /** * Build Euclid's Elements Book IV discourse JSON and Mermaid charts. * 7 definitions, 16 propositions. Inscribed/circumscribed figures. * Joyce: IV.10←IV.1,IV.5,II.11; IV.11←IV.2,IV.10; IV.12←IV.11; IV.16←IV.1,IV.2,IV.11. * All rely on Books I and III. * * Charts: 2. Chart 1: Defs + Props 1-5. Chart 2: Props 6-16. */ const fs = require('fs'); const path = require('path'); const DEFS = [ { n: 1, short: "Inscribe in circle", full: "Rectilinear figure inscribed in circle when each vertex on circumference" }, { n: 2, short: "Circumscribe about circle", full: "Figure circumscribed about circle when each side touches circle" }, { n: 3, short: "Inscribe circle in figure", full: "Circle inscribed in figure when each side touches circle" }, { n: 4, short: "Circumscribe circle about figure", full: "Circle circumscribed about figure when each vertex on circumference" }, { n: 5, short: "Inscribe in figure", full: "Figure inscribed in figure when each vertex of inner on sides of outer" }, { n: 6, short: "Circumscribe about figure", full: "Figure circumscribed about figure when each side of outer touches inner" }, { n: 7, short: "Inscribe line in circle", full: "Straight line inscribed in circle when its ends on circumference" } ]; const PROPS = [ { n: 1, short: "Fit line in circle", full: "To fit into given circle a straight line equal to given, not greater than diameter" }, { n: 2, short: "Inscribe triangle in circle", full: "To inscribe in given circle a triangle equiangular with given triangle" }, { n: 3, short: "Circumscribe triangle about circle", full: "To circumscribe about given circle a triangle equiangular with given" }, { n: 4, short: "Inscribe circle in triangle", full: "To inscribe a circle in a given triangle" }, { n: 5, short: "Circumscribe circle about triangle", full: "To circumscribe a circle about a given triangle" }, { n: 6, short: "Inscribe square in circle", full: "To inscribe a square in a given circle" }, { n: 7, short: "Circumscribe square about circle", full: "To circumscribe a square about a given circle" }, { n: 8, short: "Inscribe circle in square", full: "To inscribe a circle in a given square" }, { n: 9, short: "Circumscribe circle about square", full: "To circumscribe a circle about a given square" }, { n: 10, short: "Isosceles triangle, base angles double", full: "To construct isosceles triangle with each base angle double the remaining" }, { n: 11, short: "Inscribe pentagon in circle", full: "To inscribe an equilateral equiangular pentagon in a given circle" }, { n: 12, short: "Circumscribe pentagon about circle", full: "To circumscribe an equilateral equiangular pentagon about a given circle" }, { n: 13, short: "Inscribe circle in pentagon", full: "To inscribe a circle in a given equilateral equiangular pentagon" }, { n: 14, short: "Circumscribe circle about pentagon", full: "To circumscribe a circle about a given equilateral equiangular pentagon" }, { n: 15, short: "Inscribe hexagon in circle", full: "To inscribe an equilateral equiangular hexagon in a given circle" }, { n: 16, short: "Inscribe 15-gon in circle", full: "To inscribe an equilateral equiangular fifteen-angled figure in a given circle" } ]; // Joyce: IV.10←IV.1,IV.5,II.11; IV.11←IV.2,IV.10; IV.12←IV.11; IV.16←IV.1,IV.2,IV.11. All use Book I, Book III. const DEPS = { 1: ["BookI", "BookIII"], 2: ["BookI", "BookIII"], 3: ["BookI", "BookIII"], 4: ["BookI", "BookIII"], 5: ["BookI", "BookIII"], 6: ["BookI", "BookIII", "Prop1"], // inscribe square uses IV.1 7: ["BookI", "BookIII", "Prop6"], 8: ["BookI", "BookIII", "Prop7"], 9: ["BookI", "BookIII", "Prop8"], 10: ["BookI", "BookIII", "Prop1", "Prop5", "PropII11"], 11: ["BookI", "BookIII", "Prop2", "Prop10"], 12: ["BookI", "BookIII", "Prop11"], 13: ["BookI", "BookIII", "Prop11"], 14: ["BookI", "BookIII", "Prop11"], 15: ["BookI", "BookIII", "Prop1"], 16: ["BookI", "BookIII", "Prop1", "Prop2", "Prop11"] }; const discourse = { schemaVersion: "1.0", discourse: { id: "euclid-elements-book-iv", name: "Euclid's Elements, Book IV", subject: "geometry", variant: "classical", description: "Inscribed and circumscribed figures: triangle, square, pentagon, hexagon, 15-gon. All depend on Books I and III. IV.10 uses II.11. Source: David E. Joyce.", structure: { books: 4, definitions: 7, propositions: 16, foundationTypes: ["definition", "foundation"] } }, metadata: { created: "2026-03-15", lastUpdated: "2026-03-15", version: "1.0.0", license: "CC BY 4.0", authors: ["Welz, G."], methodology: "Programming Framework", citation: "Welz, G. (2026). Euclid's Elements Book IV Dependency Graph. Programming Framework.", keywords: ["Euclid", "Elements", "Book IV", "inscribed", "circumscribed", "pentagon", "hexagon"] }, sources: [ { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book IV", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookIV/bookIV.html", notes: "Clark University; Logical structure" } ], nodes: [], edges: [], colorScheme: { foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, definition: { fill: "#3498db", stroke: "#2980b9" }, proposition: { fill: "#1abc9c", stroke: "#16a085" } } }; // Cross-book foundations discourse.nodes.push( { id: "BookI", type: "foundation", label: "Book I — Fundamentals of plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, { id: "BookIII", type: "foundation", label: "Book III — Theory of circles", shortLabel: "Book III", short: "Foundation", book: 3, colorClass: "foundation" }, { id: "PropII11", type: "foundation", label: "Prop. II.11 — Golden section", shortLabel: "Prop. II.11", short: "From Book II", book: 2, colorClass: "foundation" } ); // Definitions for (const d of DEFS) { discourse.nodes.push({ id: `Def${d.n}`, type: "definition", label: d.full, shortLabel: `Def. IV.${d.n}`, short: d.short, book: 4, number: d.n, colorClass: "definition" }); discourse.edges.push({ from: "BookI", to: `Def${d.n}` }); discourse.edges.push({ from: "BookIII", to: `Def${d.n}` }); } // Propositions for (const prop of PROPS) { discourse.nodes.push({ id: `Prop${prop.n}`, type: "proposition", label: prop.full, shortLabel: `Prop. IV.${prop.n}`, short: prop.short, book: 4, number: prop.n, colorClass: "proposition" }); for (const dep of DEPS[prop.n]) { discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); } } // Write JSON const dataDir = path.join(__dirname, "..", "data"); fs.mkdirSync(dataDir, { recursive: true }); fs.writeFileSync(path.join(dataDir, "euclid-elements-book-iv.json"), JSON.stringify(discourse, null, 2), "utf8"); console.log("Wrote euclid-elements-book-iv.json"); function toMermaid(filter) { const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; const nodeIds = new Set(nodes.map(n => n.id)); const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); const lines = ["graph TD"]; for (const n of nodes) { const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); } for (const e of edges) { lines.push(` ${e.from} --> ${e.to}`); } lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); if (foundIds) lines.push(` class ${foundIds} foundation`); lines.push(` class ${defIds} definition`); lines.push(` class ${propIds} proposition`); return lines.join("\n"); } function closure(propMax) { const needed = new Set(); for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); needed.add("BookI"); needed.add("BookIII"); needed.add("PropII11"); for (const d of DEFS) needed.add(`Def${d.n}`); let changed = true; while (changed) { changed = false; for (const e of discourse.edges) { if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } } } return n => needed.has(n.id); } const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); function htmlTemplate(title, subtitle, mermaid, nodes, edges) { const mermaidEscaped = mermaid.replace(//g, ">"); return ` ${title} - Mathematics Process

${title}

Mathematics Geometry & Topology Source: Euclid's Elements
← Back to Mathematics Database Euclid's Elements (all books) Euclid Book IV Index Euclid's Elements Book IV (Joyce) Programming Framework

Description

${subtitle}

Source: Euclid's Elements, Book IV (David E. Joyce, Clark University)

Dependency Flowchart

${mermaidEscaped}

Color Scheme

Gray
Book I, Book III, Prop II.11 (foundation)
Blue
Definitions
Teal
Propositions

Statistics

  • Nodes: ${nodes}
  • Edges: ${edges}

Keywords

  • Euclid
  • Elements
  • Book IV
  • inscribed
  • circumscribed
  • pentagon
  • hexagon
`; } if (fs.existsSync(GEOM_DIR)) { // Chart 1: Defs + Props 1-5 (triangle constructions) const filter1 = closure(5); const nodes1 = discourse.nodes.filter(filter1); const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); const m1 = toMermaid(filter1); const html1 = htmlTemplate( "Euclid's Elements Book IV — Propositions 1–5", "Dependency graph for definitions and propositions 1–5. Inscribe/circumscribe triangle and circle. All depend on Book I and Book III.", m1, nodes1.length, edges1.length ); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iv-props-1-5.html"), html1, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-iv-props-1-5.html"); // Chart 2: Props 6-16 (square, pentagon, hexagon, 15-gon) const filter2 = () => true; const m2 = toMermaid(filter2); const html2 = htmlTemplate( "Euclid's Elements Book IV — Propositions 6–16", "Dependency graph for propositions 6–16. Square, pentagon (IV.10 uses Prop II.11), hexagon, 15-gon. IV.11←IV.2,IV.10; IV.16←IV.1,IV.2,IV.11.", m2, discourse.nodes.length, discourse.edges.length ); fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iv-props-6-16.html"), html2, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-iv-props-6-16.html"); } else { console.log("MATH_DB not found at", GEOM_DIR, "- skipping HTML generation."); } // Book IV index page if (fs.existsSync(GEOM_DIR)) { const indexHtml = ` Euclid's Elements Book IV - Mathematics Process
← Back to Mathematics Database Euclid's Elements (all books) Euclid's Elements Book IV (Joyce)

Euclid's Elements Book IV

Inscribed and circumscribed figures: triangle, square, pentagon, hexagon, 15-gon. All depend on Books I and III. Prop IV.10 uses Prop II.11 (golden section). Dependency charts split into two views.

Propositions 1–5 Defs + triangle, circle Propositions 6–16 Square, pentagon, hexagon, 15-gon
`; fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iv.html"), indexHtml, "utf8"); console.log("Wrote geometry_topology-euclid-elements-book-iv.html"); } console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length);