Plimpton 322: Base-60 Reciprocals, Not Trigonometry, Explain Babylonian Triples — E8 Intelligence Research

FINDING: Plimpton 322 encodes reciprocal pairs of regular sexagesimal integers, generating Pythagorean triples via a parametrization that is fully explained by base-60 arithmetic, not modern trigonometry. | MATH: The tablet lists 15 rows of (a, b, c) with a² + b² = c². The standard parametrization: a = p² − q², b = 2pq, c = p² + q², where p, q are regular sexagesimal integers (i.e., of form 2^α · 3^β · 5^γ). The key insight (per Bruins, refined by arxiv 1109.3814v2) is that the tablet's columns correspond to (c/a)² and (b/a)², derived from reciprocal pairs: if x = p/q and 1/x = q/p, then (x + 1/x)/2 = (p² + q²)/(2pq) = c/b, and (x − 1/x)/2 = (p² − q²)/(2pq) = a/b. All entries are regular in base 60, meaning their reciprocals terminate in sexagesimal expansion — a purely arithmetic constraint. | CONNECTION: The regular numbers {2^α·3^β·5^γ} form a multiplicative lattice in the positive reals, isomorphic to Z³. The reciprocal pairs (x, 1/x) are symmetric under inversion — a discrete refl Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com