Plimpton 322 as a Sexagesimal Reciprocal-Pair Catalog Generating Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic table of reciprocal pairs of base-60 regular numbers, from which Pythagorean triples are generated via the standard parameterization — not a trigonometric table, but a number-theoretic catalog rooted in sexagesimal reciprocals. MATH: - Core generation: for regular numbers p, q (p > q, both 60-smooth), form the triple via: a = p² − q², b = 2pq, d = p² + q² - Bruins reconstruction: the tablet's columns give d² = (p² + q²)² and the "ratio" b/d or (d/b)², derived from the reciprocal pair (p/q, q/p). - Key identity: (p² − q²)² + (2pq)² = (p² + q²)² - Sexagesimal regular numbers: integers whose only prime factors are 2, 3, 5 (divisors of 60). Their reciprocals terminate in base-60. - Column I values (d² or (d/a)²) range from ~1.4142² to ~1.4142² × ... — actually the ratios (b/d)² span from ~0.7854 to ~0.9992, i.e., angles from ~45° down to ~30°. - The "missing pairs" in Bruins: the new scheme (arXiv 1109.3814) accounts for them by a natural modi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com