Plimpton 322: A Sexagesimal Secant Table Generating 15 Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 encodes a sexagesimal geometric progression of secants (or squared secants) derived from reciprocal pairs, generating 15 Pythagorean triples with decreasing inclination. | MATH: The tablet lists columns of (a, b, c) in sexagesimal, where a = 2pq, b = p² - q², c = p² + q² for regular sexagesimal reciprocals (p, q). The key ratio is (c/a)² = sec²(θ), forming a decreasing sequence: row 1 sec² ≈ 1.9834 (θ ≈ 45°), row 15 sec² ≈ 1.3872 (θ ≈ 31.9°). The generating rule uses the identity (1/x + x)/2 and (1/x - x)/2 for regular sexagesimal x. | CONNECTION: The secant progression approximates a geometric ratio near 0.786 (specifically, the ratio between successive sec² values is ~0.96–0.98, not exactly 0.786). However, the use of base-60 regular numbers (2^a·3^b·5^c) directly links to the crystallographic root system of A₂ (hexagonal lattice) and the 60° angles of equilateral triangles. The reciprocal pairs (p, q) generate rational points on the unit circle, analogous to th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com