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 = p² - q²\), \ (b = 2pq\), \ (c = p² + q²\). 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 \ (2ᵃ 3ᵇ 5ᶜ\) ), linking to crystallographic lattice symmetries (e. g. , hexagonal close-packing, root system \ (A₂\) in 2D, \ (D₃\) 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
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