Plimpton 322: Ancient Babylonian Sexagesimal Trigonometry via Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet listing 15 Pythagorean triples, likely the world's first trigonometric table based on base-60 sexagesimal ratios, not angles. MATH: - Pythagorean triples: \ (a² + b² = c²\) with integer sides. - Tablet uses normalized ratios: \ (b² / (c² - b²) \) or equivalent, generating pairs like (3, 4, 5), (5, 12, 13), (119, 120, 169). - Base-60 (sexagesimal) system: e. g. , 1;24, 51, 10 = \ (2\) approximation (1. 41421296…). - Implicit use of reciprocal pairs: \ (x + 1/x\) and \ (x - 1/x\) to generate triples, equivalent to modern secant/tangent relations. CONNECTION: - Ratios in triples correspond to slopes (rise/run) in base-60 fractions: e. g. , 0. 618 (golden ratio conjugate) appears in some triple ratios? Not directly, but base-60 fractions like 0;36, 0 = 0. 6, 0;24, 0 = 0. 4, and 0;12, 0 = 0. 2 are common. - Geometric harmony: The tablet's structure mirrors a regular 15-fold symmetry in angle increments (~4° steps) — akin to cr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com