Plimpton 322: Old Babylonian Pythagorean Triples Predate Greek Math — E8 Intelligence Research

Abstract

FINDING: Plimpton 322 reveals Old Babylonian knowledge of Pythagorean triples and possibly trigonometric ratios, predating Greek mathematics by over a millennium. | MATH: The tablet lists 15 pairs of numbers (a, c) from a² + c² = b², with b not recorded. Ratios like (119, 169) correspond to 119² + 120² = 169². The sexagesimal system (base-60) is used. The tablet's structure suggests a generating algorithm: take reciprocal pairs (p, q) with p > q, then a = p² - q², b = 2pq, c = p² + q². | CONNECTION: The ratios a/b approximate sec²(θ) or tan²(θ) for angles from ~30° to ~45°, linking to geometric harmony via the golden ratio (1.618) and its complement (0.618) in angle divisions. Base-60 aligns with 360° circles and 12-fold symmetry. | DEPTH: 9 — Direct evidence of advanced number theory and proto-trigonometry, with implications for ancient geometric understanding. FINDING: Babylonian number system is sexagesimal (base-60), using only two symbols (wedge and corner) to represent all numbe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com