Plimpton 322: A Reciprocal-Pair Table Generating Pythagorean Triples, Not Trigonometry — E8 Intelligence Research

FINDING: Plimpton 322 is a sexagesimal reciprocal-pair table generating Pythagorean triples via regular numbers, not a trigonometric table in the modern sense. | MATH: For regular sexagesimal numbers \ (p, q\) (with \ (p > q\), both having only prime factors 2, 3, 5), the triple is \ ( (a, b, c) = (p² - q², 2pq, p² + q²) \). The tablet lists 15 pairs \ ( (p, q) \) such that \ (p/q\) yields a decreasing ratio, with columns giving \ (a\), \ (c\), and \ (b\) in sexagesimal. Key constants: base-60, regular numbers of form \ (2ᵃ 3ᵇ 5ᶜ\). | CONNECTION: The reciprocal pairs \ ( (p, q) \) correspond to ratios \ (p/q\) that approximate \ (2\) and \ (3\) (e. g. , 1;24, 51, 10 = 1. 41421296. . . for \ (2\) ). These ratios appear in the geometry of the A2 root system (hexagonal lattice, angles 60°, 120°) and G2 root system (angles 30°, 150°, 60°). The sexagesimal base directly links to the crystallographic angles of hexagonal close packing (HCP) and the 60° symmetry of the A2 lattice. The ratio 0. 61 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com