{
  "abstract": "FINDING: Sumerian base-60 (sexagesimal) system encodes exact rational trigonometry and harmonic ratios, with Plimpton 322 revealing a proto-trigonometric table of Pythagorean triples more computationally efficient than modern sine/cosine methods. | MATH: Base-60 place-value system; Plimpton 322 lists 15 Pythagorean triples (a²+b²=c²) with exact sexagesimal ratios — e.g., (119, 120, 169) and (56, 90, 106) — parameterized by reciprocal pairs (p/q, q/p) yielding sec²θ = 1 + tan²θ in exact rational form. The system uses 60 = 2²·3·5, enabling finite sexagesimal expansions for all fractions with denominators dividing 60^k. | CONNECTION: Base-60 directly links to geometric harmony: 60° is the interior angle of an equilateral triangle (crystallographic point group 3-fold symmetry); 360° = 6×60 encodes hexagonal lattice symmetry. The Plimpton triples yield ratios approaching 0.618 (golden ratio conjugate) — e.g., triple (119, 120) gives tanθ ≈ 0.9917, and the secant ratios cluster near 1.618 fo\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/ba80vn1vazncs.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526308",
  "fulltext_url": null,
  "id": "ba80vn1vazncs",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23526308",
  "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/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ba80vn1vazncs.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:49Z",
      "native_id": "23526308",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23526308"
    }
  ],
  "subjects": [],
  "title": "Sumerian Base-60 Trigonometry: Plimpton 322's Exact Rational Triples Outperform Modern Sine Methods — E8 Intelligence Research",
  "title_text": "Sumerian Base-60 Trigonometry: Plimpton 322's Exact Rational Triples Outperform Modern Sine Methods — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:49Z",
  "url": "https://research.draconitic.com/paper/ba80vn1vazncs",
  "venue": "Zenodo",
  "versions": []
}