Plimpton 322: Ancient Babylonian Sexagesimal Trigonometry, Not Angles — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing 15 rows of Pythagorean triples, likely representing the earliest known trigonometric table based on sexagesimal (base-60) ratios, not angles. | MATH: The tablet lists pairs (a, c) from triples (a, b, c) with a² + b² = c². In modern notation, each row corresponds to a ratio (c/a)² and (b/a)², or equivalently sec²θ and tan²θ for a right triangle. The sexagesimal values yield exact rational numbers, e.g., row 1: a=119, b=120, c=169 (ratio c/a = 169/119 ≈ 1.420), and the tablet's columns are derived from reciprocal pairs (p, q) with p/q generating triples via: a = p² − q², b = 2pq, c = p² + q². The tablet's ordering is by decreasing (c/a)², from ~1.98 down to ~1.39, in regular sexagesimal fractions. | CONNECTION: The triples are generated by reciprocal pairs in base-60, where "regular" numbers (those whose reciprocals terminate in sexagesimal) are used. This links directly to the golden ratio family: the ratio (c+a) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com