Babylonian Exact Ratios, Not Angles, Forge Proto-Trigonometry in Plimpton 322 — E8 Intelligence Research

FINDING: Babylonian base-60 (sexagesimal) positional notation and Plimpton 322 reveal a proto-trigonometric table based on exact ratios, not angles. | MATH: Base-60 place value (e.g., 1,0 = 60; 0;30 = 1/2). Plimpton 322 contains 15 rows of Pythagorean triples (a² + b² = c²) with exact sexagesimal reciprocals, e.g., (119, 120, 169) and (4961, 6480, 8161). Ratios of sides yield sec²(θ) values: 1;59,0,15 = 1.9834, 1;56,56,58,14,50,6,15 ≈ 1.949, down to 1;15,33,45 ≈ 1.262. | CONNECTION: Base-60 directly encodes 1/60, 1/3600 — fractions of the circle (360° = 6×60). The triples correspond to rational points on the unit circle: (x/c, y/c) = (119/169, 120/169) ≈ (0.704, 0.710) — near the golden ratio's reciprocal 0.618 but not exact. However, the ratio 1.9834 ≈ 2 − 0.0166, and 1.262 ≈ √(1.618) − 0.010 — no exact golden ratio appears. Crystallographic link: sexagesimal divisors (2,3,5) generate the 60° and 120° angles of hexagonal lattices (honeycomb, graphene, ice Ih). | DEPTH: 8 — Plimpton 32 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com