Babylonian Base-60 System: Superior Arithmetic and Plimpton 322's Pythagorean Triples — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Babylonian base-60 (sexagesimal) system provided superior computational power for arithmetic, geometry, and astronomy, with Plimpton 322 revealing advanced Pythagorean triples. | MATH: Base-60 factorization: 60 = 2² × 3 × 5 (highly composite, 12 divisors: 1,2,3,4,5,6,10,12,15,20,30,60). Reciprocal pairs (e.g., 1/60, 1/30, 1/20, 1/15, 1/12, 1/10) yield terminating sexagesimal fractions. Plimpton 322: columns of Pythagorean triples (a,b,c) with a² + b² = c², parameterized by reciprocal pairs (p/q, q/p) — equivalent to modern formula: a = p² − q², b = 2pq, c = p² + q². Cubic equations (BM 85200, YBC 4669) solved via geometric dissection and reciprocal substitution. | CONNECTION: Base-60 directly encodes the golden ratio's continued fraction structure: φ = [1;1,1,1,...] — sexagesimal expansion of φ = 1;36,54,33,20,... (1 + 36/60 + 54/3600 + ...). The ratio 0.618 (φ−1) appears in Babylonian reciprocal tables as 37;03,41,54,... (0.618055...). 60's divisors include 12 and 30 — crysta Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212148934
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