Babylonian Tablet Plimpton 322: Ancient Sexagesimal Trigonometry Predating Greek Math — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing 15 rows of Pythagorean triples, generated via a sexagesimal (base-60) algorithm that predates Greek trigonometry by over a millennium. | MATH: The tablet lists triples (a, b, c) satisfying a² + b² = c². In modern notation, the rows correspond to (p² − q², 2pq, p² + q²) for regular sexagesimal p, q. The surviving columns give (b²/(c²−b²)) — i.e., the squared secant or cotangent ratios — in base-60. Key constants: 1;59,15 = 1.9875 (row 1), 1;56,56,58,14,56,15 ≈ 1.949 (row 2), descending to 0;45 = 0.75 (row 15). The ratios b/c and a/c are rational approximations to sine/cosine, with the tablet effectively a trigonometric table of exact rational values. | CONNECTION: The triples are generated from reciprocal pairs (p, q) where p/q and q/p are regular sexagesimal numbers — this is a lattice structure on the rational points of the unit circle. The ratios b/c correspond to tan²(θ) or cot²(θ) in base-60, directly linkin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com