Plimpton 322: Babylonian Secant-Squared Table, Not Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian sexagesimal table of secant-squared (or tangent-squared) ratios for 15 right triangles, generated by reciprocal pairs (p, q) in base-60, not a primitive Pythagorean triple list. MATH: - Each row corresponds to a normalized right triangle with short side \( s \), long side \( l \), diagonal \( d \). - The tablet lists \( (d/l)^2 \) (secant²) and \( (s/l)^2 \) (tangent²) in sexagesimal. - Generation rule: choose regular sexagesimal reciprocals \( p > q \), with \( p, q \) in base-60 (e.g., \( p = 2, q = 1 \) gives \( s = p^2 - q^2 = 3 \), \( l = 2pq = 4 \), \( d = p^2 + q^2 = 5 \)). - The rows are ordered by decreasing \( (d/l)^2 \) from ~1.9834 (row 1) to ~1.3872 (row 15), corresponding to angles from ~45° down to ~30°. - Key constants: sexagesimal base 60; regular numbers (2,3,5-smooth) enable exact reciprocals. - The "missing pairs" in Bruins' reconstruction are explained by a modified scheme (arXiv:1109.3814) that predicts row Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com