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 \((a, b, c) = (p^2 - q^2, 2pq, p^2 + q^2)\). 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 \(2^a 3^b 5^c\). | 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