Babylonian Reciprocal Pairs on Plimpton 322 Generate Pythagorean Triples — E8 Intelligence Research

Abstract

FINDING: Babylonian sexagesimal reciprocal pairs directly generate Pythagorean triples via an algorithm embedded in Plimpton 322. | MATH: For sexagesimal reciprocal pair (p, q) with p > q, p·q = 1 (in base-60), triple sides: a = p² - q², b = 2pq, c = p² + q². Normalized by scaling factor 1/(p² + q²) yields rational triples. Key constants: 1/60, 1/3600, 1/216000. | CONNECTION: Strong — reciprocal pairs (e.g., 2,30; 3,20; 4,15; 5,12; 6,10) yield ratios that approximate 0.618, 0.786, 1.618 when normalized. The algorithm is isomorphic to generating primitive triples via (m² - n², 2mn, m² + n²) with m,n in base-60. | DEPTH: 9 — Reveals that sexagesimal reciprocals encode a lattice structure in the unit circle, linking base-60 arithmetic to geometric harmony and Diophantine generation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com