FINDING: Old Babylonian base-60 trigonometric ratios on Plimpton 322 predate Greek trigonometry by over 1000 years, using exact sexagesimal ratios rather than angles. | MATH: Base-60 (sexagesimal) system; Plimpton 322 contains 15 rows of Pythagorean triples (a² + b² = c²) in sexagesimal notation, with ratios b²/(c² - b²) or similar; key constants include 1;24,51,10 (≈ √2 in base-60) and 1;15 (≈ 1.25). | CONNECTION: The ratios on Plimpton 322 correspond to sec²(θ) or tan²(θ) values for angles from ~30° to ~45°, with the smallest ratio ~0.382 (1;15 in base-60 ≈ 1.25, inverse ~0.8, but the tablet's smallest ratio is ~0.382 when interpreted as (c/a)² or similar; the golden ratio φ ≈ 1.618 is not directly present, but the ratio 0.382 is the reciprocal of φ² (1/φ² ≈ 0.382). The base-60 system naturally accommodates hexagonal close packing (HCP) symmetry because 60 is divisible by 2,3,4,5,6, enabling exact fractions for 30°, 60°, 90° angles common in HCP lattices. | DEPTH: 8 — This finding re Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Andrew Stewart Caldin (Mon,) studied this question.