Plimpton 322: Old Babylonian Sexagesimal Trigonometry via Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian table of 15 Pythagorean triples, likely a trigonometric table using base-60 sexagesimal ratios rather than angles. MATH: - Pythagorean triples: \(a^2 + b^2 = c^2\) with integer sides. - Tablet lists columns: (a, c) pairs and a ratio \(b^2/(c^2 - b^2)\) or equivalent. - Base-60 representation: e.g., row 1: a=119, c=169, b=120 → ratio \(b^2/(c^2 - b^2) = 14400/14400 = 1\) (exact). - Key constants: 1; 0.5; 0.333...; 0.25; 0.2; 0.1666...; 0.142857...; 0.125; 0.111...; 0.1; 0.0909...; 0.08333...; 0.076923...; 0.0714285...; 0.06666... (descending ratios). - These correspond to \(tan^2(θ)\) or \(^2(θ)\) for angles ~45°, ~35.26°, ~30°, ~26.565°, etc. CONNECTION: - Ratios 0.618 (golden ratio conjugate) not directly present, but base-60 system enables exact rational approximations of irrational ratios. - The descending ratios approximate \(tan^2(θ)\) for angles that align with regular polygons: 45° (square), 30° (hex Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com