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

FINDING: Plimpton 322 is a 15-row Old Babylonian table of Pythagorean triples, likely a sexagesimal trigonometric table covering a specific angular range (roughly 45° down to 30°), not merely a list of triples. | MATH: Each row corresponds to a rational secant² (or tangent²) in base-60. The tablet's columns encode (b²−a², 2ab, a²+b²) for integer a,b. The angle θ satisfies tan²θ = (b²−a²)/(2ab) or similar; the rows are ordered by decreasing secant (increasing angle from ~45° to ~30°). Key constants: 1;59,0,15 (≈1.9834) down to 1;33,45 (≈1.5625) — these are sec² values. The sexagesimal base-60 is intrinsic. | CONNECTION: The angular range 45°→30° corresponds to tangent values from 1 down to 1/√3 ≈ 0.577. The reciprocal pairs in the triples (e.g., 12/5 and 5/12) yield tangent and cotangent, whose product = 1. The ratio 0.618 (golden ratio conjugate) appears as an approximation in some triples (e.g., 119/120 ≈ 0.9917, but more relevantly, the tablet's structure uses reciprocal pairs — a ha Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com