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: \(a^2 + b^2 = c^2\) with integer sides. - Tablet uses normalized ratios: \(b^2 / (c^2 - b^2)\) 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