Babylonian Base-60 Math: Superior Fractions and Advanced Pythagorean Triples — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Babylonian base-60 (sexagesimal) mathematics provided a superior computational framework for fractions and astronomical calculation, with Plimpton 322 revealing advanced Pythagorean triples. | MATH: Base-60 prime factorization: 60 = 2² × 3 × 5; reciprocal pairs (e.g., 1/60, 1/30, 1/20, 1/15, 1/12, 1/10) yield terminating sexagesimal expansions; Plimpton 322 contains 15 rows of Pythagorean triples (a² + b² = c²) generated via parameters p, q (likely p² − q², 2pq, p² + q²), with ratios like 119/120, 3367/4825, 4601/4800 — all normalized to hypotenuse ≈ 1. | CONNECTION: Base-60 directly encodes the 360° circle (6×60), enabling exact division into 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 parts — a harmonic lattice of divisors. The reciprocal pairs (e.g., 1/60 = 0.016666…, 1/30 = 0.0333…) mirror the sexagesimal expansion of 1/φ ≈ 0.6180339… (which in base-60 is 0;37,04,55,20 — a terminating-like sequence due to φ's algebraic nature). Plimpton 322's normalized triples (hypotenuse ≈ 1) are 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: W7212083194
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