Plimpton 322 Decoded: Base-60 Secant-Squared Table via Reciprocal Pairs — E8 Intelligence Research

FINDING: Plimpton 322 encodes a precise table of secant-squared values (1 + tan²θ) for 15 right triangles, generated via reciprocal pairs in base-60, not merely Pythagorean triples. | MATH: Each row yields (a, b, c) with c² = a² + b²; the tablet lists (c/a)² = sec²θ = 1 + (b/a)². In base-60, the sexagesimal values are exact: e.g., row 1 gives sec²θ = 1.9834027… (base-60: 1;59,0,15), row 15 gives sec²θ = 1.387352… (base-60: 1;23,13,46,40). The generating algorithm uses reciprocal pairs (p, q) with p·q = 1 (in base-60), producing triples via (p²−q², 2pq, p²+q²) scaled to integer form. | CONNECTION: The sec² values cluster near 1.983, 1.949, 1.918, … down to 1.387 — these are NOT golden-ratio harmonics (φ=1.618, φ²=2.618, 1/φ=0.618). However, the base-60 system itself is deeply tied to 60 = 2²·3·5, the smallest number with 12 divisors, enabling exact division by 2,3,4,5,6,10,12,15,20,30 — a lattice of rational points on the unit circle (rational parametrization t = tan(θ/2)). The sec² val Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com