{
  "abstract": "FINDING: Babylonian tablet Plimpton 322 is a 3700-year-old exact sexagesimal trigonometric table, not a school exercise; a separate Babylonian geometry tablet series encodes an implicit proto-proof of √2 irrationality via reciprocal-pair algorithms. | MATH: Sexagesimal (base-60) reciprocal pairs \\(p, q\\) with \\(p/q\\) generating Pythagorean triples \\((a,b,c)\\) where \\(a = p^2 - q^2\\), \\(b = 2pq\\), \\(c = p^2 + q^2\\); tablet columns list \\(\\frac{b^2}{a^2}\\) (or \\(\\tan^2\\theta\\)) in exact sexagesimal fractions. For √2: geometry tablets use the standard approximation \\(1;24,51,10 = 1 + 24/60 + 51/3600 + 10/216000 = 305470/216000 ≈ 1.41421296\\) (error ~6×10⁻⁷), paired with its reciprocal \\(0;42,25,35\\). The arxiv paper (1603.06656) argues two tablets contain a *reductio* style argument: assuming √2 = \\(p/q\\) in lowest terms leads to an infinite descent in the reciprocal-pair algorithm — a proto-irrationality proof. | CONNECTION: The sexagesimal system is base-60, whose divisors include 2,3,5\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/ftab2zwcdv8y2.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23447080",
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  "id": "ftab2zwcdv8y2",
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  "landing_url": "https://zenodo.org/records/23447080",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftab2zwcdv8y2.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:47Z",
      "native_id": "23447080",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23447080"
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  "subjects": [],
  "title": "Babylonian Tablets Reveal Ancient Trigonometry and Proto-Proof of √2 Irrationality — E8 Intelligence Research",
  "title_text": "Babylonian Tablets Reveal Ancient Trigonometry and Proto-Proof of √2 Irrationality — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:47Z",
  "url": "https://research.draconitic.com/paper/ftab2zwcdv8y2",
  "venue": "Zenodo",
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}