Plimpton 322: Old Babylonian Trigonometry via Exact Sexagesimal Ratios — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian trigonometric table based on exact sexagesimal ratios, not angles, using Pythagorean triples to compute reciprocal pairs for right triangles. MATH: - 15 rows of Pythagorean triples (a, b, c) with a < b, satisfying a² + b² = c². - Sexagesimal (base-60) system: ratios expressed as (b/a) and (c/a) in sexagesimal fractions. - Key ratios derived: b/a = 1; 1.5; 1.333...; 1.25; 1.2; etc., corresponding to sec²(θ) = (c/a)². - No explicit angles; instead, the tablet lists (c/a)² values (e.g., 1.9834027... in sexagesimal 1;59,0,15). - Implicit use of reciprocal pairs: if x = b/a, then 1/x = a/b, generating complementary triangles. CONNECTION: - Ratios 0.618, 1.618 appear in the reciprocal structure: e.g., b/a = 1.618 (golden ratio) corresponds to a/b = 0.618, linking to geometric harmony. - Base-60 system aligns with 360° circle division, enabling precise trigonometric interpolation. - No direct crystallographic symmetry, but the recip Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com