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 \(2^a 3^b 5^c\) (divisors of 60). Primitive Pythagorean triples (a,b,c) satisfy \(a^2 + b^2 = c^2\) with gcd(a,b,c)=1; Dickson's method: find integers r,s,t with \(r^2 = 2st\), 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