Plimpton 322: Ancient Babylonian Sexagesimal Trigonometric Table — E8 Intelligence Research

FINDING: Plimpton 322 is a 15-row Old Babylonian table of Pythagorean triples, likely generated by a sexagesimal (base-60) parameterization — not merely a list, but a structured trigonometric or ratio table. | MATH: The tablet encodes triples (a, b, c) with c² = a² + b², in sexagesimal. The standard reconstruction uses parameters p > q (coprime, opposite parity) giving a = p² − q², b = 2pq, c = p² + q². The tablet's columns correspond to (b²/c²) or (b/c)² — i.e., squared secant/tangent ratios. Row 1: (119, 120, 169) → ratio b²/c² = 14400/28561 ≈ 0.5042 (sexagesimal: 0;30,15). Row 11: (45, 60, 75) → b²/c² = 3600/5625 = 0.64 = 0;38,24. The tablet's first column lists values of (c/a)² = 1 + (b/a)², ranging from ~1.98 down to ~1.39, in decreasing order — a monotonic sequence of squared cosecant ratios. | CONNECTION: The ratios 0.382, 0.618, 0.786, 1.618, 2.618 do NOT appear directly in Plimpton 322's known rows. However, the base-60 system is fundamental: 60 = 2²·3·5, whose divisors genera Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com