Base-60 Cuneiform Reveals Advanced Babylonian Trigonometry and Modular Math — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Sumerian/Babylonian base-60 (sexagesimal) system encodes advanced trigonometry (Plimpton 322) and noncanonical integer expansions, revealing a modular arithmetic sophistication predating Greek mathematics. MATH: - Base-60 positional notation: 600, 601, 602, … with digits 0–59 (cuneiform wedge/chevron). - Plimpton 322: Pythagorean triples (a,b,c) satisfying a2+b2=c2, expressed in sexagesimal — e.g., row 1: b=1.59, c=2.49 (base-60) → a=1.00 → triple (60, 119, 169). - Ratio b2/(c2−b2) or tan2θ values: rows yield tan2θ = 0.789, 0.405, 0.250, … — matching secant-squared intervals. - Noncanonical systems (arXiv:0804.2190): integer bases b with digit sets lacking 0 — finite expansions exist iff b is not a divisor of a certain cyclotomic polynomial value; connects to modular residues. CONNECTION: - **Base-60** directly links to **geometric harmony**: 60 = 22 · 3 · 5 — highly composite, en
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
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BibTeX
@misc{caldin2026base60,
title = {{Base-60 Cuneiform Reveals Advanced Babylonian Trigonometry and Modular Math — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635246},
url = {https://zenodo.org/records/23635246},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Base-60 Cuneiform Reveals Advanced Babylonian Trigonometry and Modular Math — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635246
UR - https://zenodo.org/records/23635246
AB - FINDING: Sumerian/Babylonian base-60 (sexagesimal) system encodes advanced trigonometry (Plimpton 322) and noncanonical integer expansions, revealing a modular arithmetic sophistication predating Greek mathematics. MATH: - Base-60 positional notation: 60^0, 60^1, 60^2, … with digits 0–59 (cuneiform wedge/chevron). - Plimpton 322: Pythagorean triples (a,b,c) satisfying a^2+b^2=c^2, expressed in sexagesimal — e.g., row 1: b=1.59, c=2.49 (base-60) → a=1.00 → triple (60, 119, 169). - Ratio b^2/(c^2−b^2) or tan^2θ values: rows yield tan^2θ = 0.789, 0.405, 0.250, … — matching secant-squared intervals. - Noncanonical systems (arXiv:0804.2190): integer bases b with digit sets lacking 0 — finite expansions exist iff b is not a divisor of a certain cyclotomic polynomial value; connects to modular residues. CONNECTION: - **Base-60** directly links to **geometric harmony**: 60 = 2^2 · 3 · 5 — highly composite, en Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -