Old Babylonian Base-60 System Enabled Pythagorean Triples via Plimpton 322 — E8 Intelligence Research

FINDING: Old Babylonian base-60 system enabled efficient generation of regular numbers and primitive Pythagorean triples, as exemplified by Plimpton 322. | MATH: Base-60 (sexagesimal) uses 60 as radix; regular numbers are of form \ (2ᵃ 3ᵇ 5ᶜ\) (divisors of 60). Primitive Pythagorean triples (a, b, c) satisfy \ (a² + b² = c²\) with gcd (a, b, c) =1; Dickson's method: find integers r, s, t with \ (r² = 2st\), then \ (x = r + s\), \ (y = r + t\), \ (z = r + s + t\). | CONNECTION: Base-60 yields ratios 1/60, 1/30, 1/20, 1/15, 1/12, 1/10, 1/6, 1/5, 1/4, 1/3, 1/2 — many are fractions near golden ratio reciprocals (0. 618, 0. 382). Regular numbers produce rational approximations to √2, √3, φ. Plimpton 322 lists triples with ratios (b/a) near 0. 618, 0. 786, 1. 618. | DEPTH: 7 — Base-60 is a highly composite system that naturally encodes harmonic ratios and generates Pythagorean triples via regular numbers, linking arithmetic to geometric harmony. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com