Babylonian Tablet Predates Greek Trigonometry by 1,000 Years — E8 Intelligence Research

Abstract

FINDING: Babylonian Plimpton 322 tablet encodes exact sexagesimal Pythagorean triples — the earliest known trigonometric table, predating Greek trigonometry by over 1,000 years. | MATH: Sexagesimal (base-60) system; Pythagorean triples (a² + b² = c²) expressed as ratios of sides; tablet lists 15 rows of (short side, diagonal) pairs with (long side) implicit. Key ratios: sec²(θ) = (c/b)², tan²(θ) = (a/b)² — values like 1.9834027…, 1.9491585…, 1.9189859… (from row 1–3). Exact triples: (119, 120, 169), (3367, 3456, 4825), (4601, 4800, 6649) — all in sexagesimal fractions. | CONNECTION: The ratios (c/b)² and (a/b)² correspond to sec² and tan². Notably, row 1 gives sec² ≈ 1.9834, and row 15 gives sec² ≈ 1.0000 — a monotonic sweep from ~45° to ~30°. The sexagesimal base 60 yields exact fractions (e.g., 1/60, 1/3600) — a lattice of rational points on the unit circle, analogous to crystallographic rational points in root systems (e.g., A₂ lattice, hexagonal symmetry). The triple (119,120,169) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com