Old Babylonian Base-60 Arithmetic Enabled Precision Tables and Pythagorean Triples — E8 Intelligence Research

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 (2^a·3^b·5^c) yield terminating reciprocals; Plimpton 322 contains 15 rows of Pythagorean triples (a^2 + b^2 = c^2) 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 φ^2 ≈ 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