Plimpton 322: A Reciprocal-Pair Generator, Not a Trig Table — E8 Intelligence Research

FINDING: Plimpton 322 is a sexagesimal reciprocal-pair generator for Pythagorean triples, not a trigonometric table; its algorithm uses regular numbers to produce normalized diagonals and sides. MATH: For regular numbers \(p, q\) (sexagesimal reciprocals, \(p · q = 1\) in base-60), generate triple: \(a = p^2 - q^2\), \(b = 2pq\), \(c = p^2 + q^2\). Tablet lists \(c/a\) (diagonal/short side) as sexagesimal fractions, e.g., row 1: \(c/a ≈ 1.9834027...\) (sexagesimal 1;59,0,15). Missing pairs explained by Bruins' modification: generator pairs \((p,q)\) with \(p/q\) near \(√2\) produce the 15 rows. CONNECTION: No explicit golden ratio (0.618, 1.618) or harmonic ratios (0.382, 0.786, 2.618) appear. However, the reciprocal-pair method inherently uses base-60 regular numbers (divisors of \(2^a 3^b 5^c\)), linking to crystallographic lattice symmetries (e.g., hexagonal close-packing, root system \(A_2\) in 2D, \(D_3\) in 3D). The normalized diagonal \(c/a\) values approxima Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com