Plimpton 322: A Sexagesimal Trigonometric Table of Reciprocal Pairs — E8 Intelligence Research

FINDING: Old Babylonian Plimpton 322 encodes a sexagesimal trigonometric table based on Pythagorean triples, not angles, revealing a lattice geometry of reciprocal pairs. | MATH: Pythagorean triples (a² + b² = c²) generated from reciprocal pairs (p, q) in base-60: a = p² - q², b = 2pq, c = p² + q². Plimpton 322 lists 15 triples with c²/b² ratios (e.g., 1.9834027…, 1.9491585…). Key constants: 1;24,51,10 (√2 ≈ 1.41421296) and 1;59,0,15 (√3 ≈ 1.7320508) appear in OB tablets. | CONNECTION: Sexagesimal lattice geometry yields 12-fold symmetry via regular hexagon tiling (60° angles). The reciprocal pairs (p, q) correspond to rational points on the unit circle, linking to the golden ratio φ = 1.618… through 5-fold symmetry in base-60 (60 = 2²×3×5). Ratios 0.618, 0.382 appear in OB area calculations for regular pentagons. | DEPTH: 8 — Directly ties Pythagorean triples to sexagesimal lattice, revealing a pre-Hellenistic trigonometric system based on ratios, not angles. Implicitly connects to cr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com