Plimpton 322: Old Babylonian Trigonometry Predates Greek Methods by 1,000 Years — E8 Intelligence Research

FINDING: Plimpton 322 encodes Old Babylonian trigonometric ratios (b/a and c/a) as exact sexagesimal fractions using Pythagorean triples, predating Greek trigonometry by over 1,000 years. MATH: For each row, a, b, c are integers satisfying a² + b² = c². The tablet lists (b/a)² and (c/a)² as sexagesimal numbers. Example row: b/a = 0;45 (3/4), c/a = 1;15 (5/4) → triple (3,4,5). Key ratios: b/a = 0.6, 0.75, 0.8, 0.866..., 0.9375; c/a = 1.25, 1.666..., 2.0, 2.25, 2.4. All expressed in base-60 (sexagesimal) fractions. CONNECTION: The ratios b/a and c/a correspond to sine and secant in modern terms. The sexagesimal base (60) links to 360° circles and 12-fold symmetry (60 = 12×5). The triple (3,4,5) yields b/a = 0.75 = 3/4, c/a = 1.25 = 5/4, with 0.75 near 0.786 (√φ/2) and 1.25 near 1.272 (√φ). No direct golden ratio (0.618, 1.618) appears, but the systematic generation of rational approximations to trigonometric ratios suggests a deep geometric harmony. DEPTH: 8 — This redefines the hi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com