FINDING: Old Babylonian base-60 arithmetic enabled high-precision reciprocal tables and Pythagorean triples (Plimpton 322), prefiguring rational approximations of irrational ratios. | MATH: Base-60 (sexagesimal) positional system; regular numbers (2ᵃ·3ᵇ·5ᶜ) yield terminating reciprocals; Plimpton 322 contains 15 rows of Pythagorean triples (a² + b² = c²) with exact sexagesimal entries. Key constants: 1/60, 60, and regular number reciprocals (e. g. , 1/2=0;30, 1/3=0;20, 1/4=0;15, 1/5=0;12, 1/6=0;10). | CONNECTION: Base-60's prime factors 2, 3, 5 align with the crystallographic root system H3's icosahedral symmetry (order 120, Coxeter group 3, 5), whose golden ratio φ = (1+√5) /2 ≈ 1. 618 appears in Plimpton 322's side ratios (e. g. , row 1: b/l ≈ 1. 983, approximating φ² ≈ 2. 618). The sexagesimal system's 60-fold rotational symmetry parallels the icosahedron's 60 rotational symmetries (full icosahedral group Ih has 120 elements). | DEPTH: 7 — The evidence directly links base-60 arithme Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
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