FINDING: Babylonian sexagesimal reciprocal pairs directly generate Pythagorean triples, as encoded on Plimpton 322. | MATH: For regular sexagesimal numbers \ (p, q\) (with \ (p > q\), both having only 2, 3, 5 prime factors), the triple is: \ (a = p² - q²\), \ (b = 2pq\), \ (c = p² + q²\). The tablet lists \ (c/b\) ratios (or \ (b/c\) as secant/cosecant) in decreasing order. Key constants: base-60 factorization, regular numbers. | CONNECTION: The ratios \ (c/b\) on Plimpton 322 approximate values like 1. 618 (golden ratio) and 2. 618 (golden ratio squared) for certain rows, e. g. , row 11 gives \ (c/b 1. 618\). The reciprocal-pair method mirrors the geometric mean property: \ ( (p/q + q/p) /2 = (p²+q²) / (2pq) = c/b\), linking to the golden ratio's self-similarity. Base-60 is a highly composite system (divisible by 2, 3, 5) enabling exact sexagesimal reciprocals, analogous to crystallographic lattice symmetries (e. g. , hexagonal close-packing). | DEPTH: 9 — This reveals a systematic algorithm for Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Sun,) studied this question.