{
  "abstract": "FINDING: Plimpton 322 encodes exact sexagesimal reciprocal pairs that generate Pythagorean triples via a tangent half-angle parametrization of the unit circle, predating Greek trigonometry by a millennium. | MATH: The tablet lists 15 rows of (a, c) values with b² = c² − a². The underlying parametrization is equivalent to: x = (1 − t²)/(1 + t²), y = 2t/(1 + t²), where t = p/q in sexagesimal. The reciprocal pairs (p, q) satisfy p·q = 60^k (regular numbers), yielding exact rational points on the unit circle. Key ratios: c/a values range from 1.983 to 1.387 (sexagesimal: 1;59,00,15 to 1;23,13,46). The diagonal-to-short-side ratio (c/b) corresponds to tan(θ/2) = q/p, with θ the acute angle. | CONNECTION: The reciprocal pairs are regular sexagesimal numbers — their prime factors are only 2, 3, 5 — linking directly to base-60 arithmetic. The tangent half-angle substitution is the rational parametrization of the unit circle, whose integer solutions (Pythagorean triples) are lattice poi\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0r4w9hbjjtccj.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23447128",
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  "id": "0r4w9hbjjtccj",
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  "landing_url": "https://zenodo.org/records/23447128",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0r4w9hbjjtccj.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:47Z",
      "native_id": "23447128",
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      "url": "https://zenodo.org/records/23447128"
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  "title": "Babylonian Tablet Plimpton 322: Ancient Sexagesimal Trigonometry Predates Greeks — E8 Intelligence Research",
  "title_text": "Babylonian Tablet Plimpton 322: Ancient Sexagesimal Trigonometry Predates Greeks — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:47Z",
  "url": "https://research.draconitic.com/paper/0r4w9hbjjtccj",
  "venue": "Zenodo",
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}