{
  "id": "pythagorean-theorem",
  "domain": "named-results",
  "also_in_domain": "geometry",
  "type": "Theorem",
  "title": "Pythagorean Theorem",
  "slug": "pythagorean-theorem",
  "url": "/mathematics/named-results/pythagorean-theorem/",
  "statement": "In a right-angled triangle with legs a, b and hypotenuse c: a² + b² = c².",
  "summary": "The relationship between the sides of a right triangle. Known to Babylonian (c. 1800 BCE), Indian (c. 800 BCE), and Chinese (c. 300 BCE) mathematicians before Greek deductive proof. One of the most proven theorems in mathematics (400+ known proofs).",
  "civilisational_record": [
    { "tradition": "Babylonian", "evidence": "Plimpton 322 tablet", "date_ce": -1800, "reference": "Robson 2001, Historia Mathematica" },
    { "tradition": "Indian", "evidence": "Baudhāyana Śulbasūtra statement", "date_ce": -800, "reference": "Plofker 2009, Mathematics in India, pp. 17–23" },
    { "tradition": "Chinese", "evidence": "Zhou Bi Suan Jing (Gōu-Gǔ theorem)", "date_ce": -300, "reference": "Cullen 1996" },
    { "tradition": "Greek", "evidence": "Euclid, Elements I.47, deductive proof", "date_ce": -300, "reference": "Heath 1956" }
  ],
  "proofs_count": "400+",
  "added_to_codex": "2026-05-27",
  "last_verified": "2026-05-27",
  "sources": [
    { "tier": 1, "citation": "Heath, T.L. (1956). Euclid: The Thirteen Books of the Elements. Vol. 1. Dover." },
    { "tier": 1, "citation": "Plofker, K. (2009). Mathematics in India. Princeton University Press.", "pages": "17–23" },
    { "tier": 1, "citation": "Robson, E. (2001). Neither Sherlock Holmes nor Babylon. Historia Mathematica, 28(3), 167–206." },
    { "tier": 2, "citation": "Cullen, C. (1996). Astronomy and Mathematics in Ancient China: The Zhou Bi Suan Jing. Cambridge University Press." },
    { "tier": 2, "citation": "Loomis, E.S. (1927). The Pythagorean Proposition. NCTM (1968 reprint)." },
    { "tier": 3, "citation": "Joseph, G.G. (2011). The Crest of the Peacock. 3rd ed. Princeton University Press.", "pages": "237–248" }
  ],
  "relationships": [
    { "type": "early_evidence", "target": "babylonian-mathematics", "label": "Plimpton 322 (c. 1800 BCE)" },
    { "type": "early_evidence", "target": "baudhayana-sulbasutra", "label": "Baudhāyana Śulbasūtra (c. 800 BCE)" },
    { "type": "generalised_by", "target": "law-of-cosines", "label": "Law of Cosines" },
    { "type": "related", "target": "fermats-last-theorem", "label": "Fermat's Last Theorem (no solutions for n ≥ 3)" }
  ],
  "entry_status": "live",
  "reading_levels_available": ["curious", "exploring", "deep_dive"],
  "completeness": 1.0,
  "codex_version": "1.1"
}