FINDING: Plimpton 322 contains 15 rows of Pythagorean triples, likely representing an early trigonometric table based on sexagesimal (base-60) ratios. MATH: - Pythagorean triples: a² + b² = c², with a < b. - Tablet lists pairs (b, c) for integer a, b, c, e.g., row 1: (119, 169) → triple (119, 120, 169). - Underlying parameterization: a = p² - q², b = 2pq, c = p² + q², with p, q regular sexagesimal numbers. - Ratios b/a (or c/a) correspond to secant/tangent values in base-60, e.g., b/a ≈ 1.0084, 1.25, 1.333..., etc. - Sexagesimal (base-60) system used for precise fractions: 1/60, 1/3600, etc. CONNECTION: - Ratios b/a approximate 1.618 (golden ratio) in some rows? No direct evidence; but the systematic generation of triples mirrors harmonic proportions. - Base-60 aligns with 360° circle and 12-fold symmetries (e.g., crystallographic point groups, icosahedral symmetry). - The triples encode rational approximations of √2, √3, φ? Not explicitly, but the method implies deep Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Andrew Stewart Caldin (Mon,) studied this question.