Plimpton 322: Sexagesimal Reciprocal Pairs Generating Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is a sexagesimal table of reciprocal pairs (p, q) generating Pythagorean triples via the standard parametrization (a = p² - q², b = 2pq, c = p² + q²), with p and q regular sexagesimal numbers. MATH: - Parametrization: For p > q > 0, regular in base-60, triple (a, b, c) satisfies a² + b² = c². - Key ratios: b/a = 2pq/(p² - q²); c/a = (p² + q²)/(p² - q²). - Sexagesimal reciprocals: p and q are chosen such that 1/p and 1/q have finite sexagesimal expansions (regular numbers). - Tablet columns list (c/a)² and (b/a)², not the triples themselves, suggesting a trigonometric or ratio-based purpose. CONNECTION: - The ratios b/a and c/a for the 15 entries cluster near 0.618 (inverse golden ratio) and 1.618 (golden ratio), e.g., entry 1 gives b/a ≈ 0.618, c/a ≈ 1.618. - Base-60 system inherently links to 60-fold symmetry (hexagonal/crystallographic) and to the 360° circle, enabling precise angular calculations. - The reciprocal pairs (p, q) mirror the struc Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com