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

FINDING: Plimpton 322 contains a systematic method for generating Pythagorean triples, likely based on reciprocal pairs in base-60, predating Greek mathematics by over a millennium. | MATH: For a normalized rectangle with short side = 1, long side = x, diagonal = y, the tablet lists (x, y) pairs satisfying y² - x² = 1. This is equivalent to generating triples (a, b, c) via a = 2pq, b = p² - q², c = p² + q², where p and q are regular sexagesimal reciprocals (p/q = 1/(q/p) in base-60). Key constants: 1; 1.5; 1.333...; 1.8; 1.666...; 2.25; 1.2; 1.125; 1.111...; 1.04; 1.01; 1.006...; 1.004...; 1.002...; 1.001... (ratios from tablet). | CONNECTION: The method relies on base-60 (sexagesimal) arithmetic, which is deeply connected to the golden ratio φ ≈ 1.618 via the regular numbers 1, 2, 3, 5 and their reciprocals. The ratio 1.618 appears as a limit of successive regular number ratios (e.g., 5/3 ≈ 1.666, 8/5 = 1.6, 13/8 = 1.625). The tablet's triples correspond to right triangles with intege Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com