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

FINDING: Plimpton 322 is a Babylonian table of 15 Pythagorean triples generated via reciprocal pairs of regular sexagesimal numbers, not a random list — the algorithm is reconstructible from the tablet's column structure. | MATH: The tablet lists (a, b, c) with a² + b² = c². The generating method: choose regular numbers x, y (in base-60, with only prime factors 2, 3, 5) such that xy = 1 (reciprocal pairs). Then set: a = (x − y)/2, b = (x + y)/2, c = 1 (or scaled). Equivalently, for x = p/q in lowest terms, a = (p² − q²)/(2pq), b = (p² + q²)/(2pq). The tablet's columns contain (b/a)², a, c — with the first column being (c/a)² = 1 + (b/a)². The 15 rows correspond to the 15 largest regular reciprocal pairs with x > y, x/y < 1.5 (or similar bound), giving the observed decreasing first-column values. | CONNECTION: Base-60 is the direct ancestor of our 360° circle and 60-minute hour. The regular numbers (2, 3, 5) are the prime factors of 60 — this is the sexagesimal lattice. The ratios in th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com