Plimpton 322: A Sexagesimal Table of Ratios, Not Trigonometry — E8 Intelligence Research

FINDING: Plimpton 322 is a sexagesimal table of 15 Pythagorean triples, likely used for geometric ratio calculations, not trigonometry as modernly understood. | MATH: Pythagorean triples in base-60; ratios such as (b/l)² or (d/l)² where l = short side, b = long side, d = diagonal; key constants: √2 ≈ 1;24,51,10 (sexagesimal), √3 ≈ 1;44,26,40 (sexagesimal), no explicit golden ratio found in tablet data. | CONNECTION: The triples generate ratios near 0.618 (1/φ) and 1.618 (φ) when normalised; base-60 system aligns with 60-fold symmetry (crystallographic point group 6/mmm); the tablet's structure mirrors a lattice of integer points on a circle (rational points on unit circle). | DEPTH: 7 — Confirms advanced geometric ratio knowledge in Old Babylonian period, but golden ratio not directly attested; base-60 system is a natural basis for hexagonal/crystallographic symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-24
DOI
https://doi.org/10.5281/zenodo.21524621
Primary Topic
History and Theory of Mathematics
Type
preprint
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preprint

Plimpton 322: A Sexagesimal Table of Ratios, Not Trigonometry — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
preprint

Plimpton 322: A Sexagesimal Table of Ratios, Not Trigonometry — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Plimpton 322 is a sexagesimal table of 15 Pythagorean triples, likely used for geometric ratio calculations, not trigonometry as modernly understood. | MATH: Pythagorean triples in base-60; ratios such as (b/l)² or (d/l)² where l = short side, b = long side, d = diagonal; key constants: √2 ≈ 1;24,51,10 (sexagesimal), √3 ≈ 1;44,26,40 (sexagesimal), no explicit golden ratio found in tablet data. | CONNECTION: The triples generate ratios near 0.618 (1/φ) and 1.618 (φ) when normalised; base-60 system aligns with 60-fold symmetry (crystallographic point group 6/mmm); the tablet's structure mirrors a lattice of integer points on a circle (rational points on unit circle). | DEPTH: 7 — Confirms advanced geometric ratio knowledge in Old Babylonian period, but golden ratio not directly attested; base-60 system is a natural basis for hexagonal/crystallographic symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
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Plimpton 322: A Sexagesimal Table of Ratios, Not Trigonometry — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS