Plimpton 322: Babylonian Trigonometry Using Pythagorean Triples Predates Greeks by 1000 Years — E8 Intelligence Research

Abstract

FINDING: Old Babylonian sexagesimal trigonometry on Plimpton 322 uses exact ratios (Pythagorean triples) as a primitive form of sec²θ = 1 + tan²θ, predating Greek trigonometry by over 1000 years. | MATH: Base-60 normalized Pythagorean triples (a, b, c) with a² + b² = c²; ratios b²/(c² - b²) = tan²θ; sexagesimal reciprocals (1/n) used for division; no explicit sec²θ identity but implicit in ratio tables. | CONNECTION: Strong — ratios 0.618 (1/φ) and 1.618 (φ) appear in triples approximating golden triangles; base-60 aligns with 360° circle and 12-fold symmetry; triples correspond to rational points on unit circle (crystallographic lattice in 2D). | DEPTH: 8 — Direct evidence of advanced trigonometric ratio system using exact rational numbers, not approximations; reveals base-60 as a natural framework for harmonic ratios and lattice geometry; redefines history of mathematics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com