Babylonian Base-60 Math Outperforms Greek Trigonometry in Exact Division — E8 Intelligence Research

FINDING: Babylonian base-60 (sexagesimal) mathematics provides a superior framework for exact division and astronomical calculation, with Plimpton 322 revealing advanced Pythagorean triples predating Greek trigonometry. | MATH: Base 60 has prime factors {2, 3, 5}, yielding 12 divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) — maximal divisibility for a number < 100. Plimpton 322 contains 15 rows of Pythagorean triples (a² + b² = c²) in sexagesimal, e.g., (119, 120, 169) and (4961, 6480, 8161), generated by reciprocal pairs (p, q) with p/q in sexagesimal fractions. Cubic equations (BM 85200, YBC 4669) solved via geometric dissection, not algebraic radicals. | CONNECTION: Base 60 directly encodes the golden ratio's continued fraction: φ = [1; 1, 1, 1, ...] — in sexagesimal, φ ≈ 1;36,54,33,34,05 (i.e., 1 + 36/60 + 54/3600 + ...), and 1/φ ≈ 0;36,54,33,34. The divisors of 60 include 12 and 30, linking to zodiacal 12-fold and 30° arcs — the ecliptic's 360° = 6 × 60. Pythagorean triples fr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-06
DOI
https://doi.org/10.5281/zenodo.22469836
Primary Topic
History and Theory of Mathematics
Type
preprint
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Babylonian Base-60 Math Outperforms Greek Trigonometry in Exact Division — E8 Intelligence Research

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

Babylonian Base-60 Math Outperforms Greek Trigonometry in Exact Division — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Babylonian base-60 (sexagesimal) mathematics provides a superior framework for exact division and astronomical calculation, with Plimpton 322 revealing advanced Pythagorean triples predating Greek trigonometry. | MATH: Base 60 has prime factors {2, 3, 5}, yielding 12 divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) — maximal divisibility for a number < 100. Plimpton 322 contains 15 rows of Pythagorean triples (a² + b² = c²) in sexagesimal, e.g., (119, 120, 169) and (4961, 6480, 8161), generated by reciprocal pairs (p, q) with p/q in sexagesimal fractions. Cubic equations (BM 85200, YBC 4669) solved via geometric dissection, not algebraic radicals. | CONNECTION: Base 60 directly encodes the golden ratio's continued fraction: φ = [1; 1, 1, 1, ...] — in sexagesimal, φ ≈ 1;36,54,33,34,05 (i.e., 1 + 36/60 + 54/3600 + ...), and 1/φ ≈ 0;36,54,33,34. The divisors of 60 include 12 and 30, linking to zodiacal 12-fold and 30° arcs — the ecliptic's 360° = 6 × 60. Pythagorean triples fr 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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