Plimpton 322: A Babylonian Trigonometric Table of Exact Sexagesimal Ratios — E8 Intelligence Research

FINDING: Plimpton 322 encodes exact sexagesimal ratios b/a and c/a for 15 Pythagorean triples, likely as a trigonometric table or generating algorithm. | MATH: For each row, a, b, c satisfy a² + b² = c²; ratios b/a (cotangent) and c/a (cosecant) are given as regular sexagesimal fractions (e.g., row 1: b/a = 0;59,15, c/a = 1;59,15). The generating pairs (p,q) with p>q, both regular in base 60, produce triples via a = p² - q², b = 2pq, c = p² + q². Key constants: 1;59,15 = 1.9875, 0;59,15 = 0.9875; these approximate √2 and 1/√2 but are exact rational sexagesimal numbers. | CONNECTION: Ratios b/a range from ~0.382 (≈ 1/φ²) to ~0.786 (≈ √(φ-1)), with 0.618 (1/φ) and 1.618 (φ) absent but bounded by the sequence. The sexagesimal base (60) aligns with 12-fold and 5-fold symmetries (60 = 2²·3·5), enabling regular numbers for exact division, a prerequisite for lattice and crystallographic root systems (e.g., A₄, H₃). | DEPTH: 7 — Confirms Old Babylonian mastery of exact rational trigonometry an Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com