Plimpton 322: Oldest Exact Trigonometric Table Predates Greek Math by 1000 Years — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing a systematic table of 15 Pythagorean triples, now proven to represent the world's first exact trigonometric table, predating Greek trigonometry by over 1000 years. MATH: The tablet lists pairs of numbers (a, c) from which the third side b of a right triangle is derived via b = sqrt(c² - a²). The ratios c/a and b/a correspond to secant and tangent functions in a base-60 (sexagesimal) system. Key constants: 1;59,15 (≈ 1.9834), 1;56,56,58,14,50,6,15 (≈ 1.949), etc. The triples are generated by the Old Babylonian method: let p > q be regular sexagesimal numbers, then a = p² - q², b = 2pq, c = p² + q². The tablet orders triples by decreasing c/a (i.e., decreasing secant angle from ~45° to ~30°). CONNECTION: The base-60 system directly links to geometric harmony: 60 is divisible by 2,3,4,5,6,10,12,15,20,30 — enabling exact fractions for angles in a circle. The ratios c/a and b/a approximate the golden ratio φ = 1.61 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com