Babylonian Trigonometry Linked to Rational Circle Parametrization via Base-60 Divisions — E8 Intelligence Research

FINDING: The rational parametrization of the unit circle — central to Babylonian/sexagesimal trigonometry — is explicitly linked to base-60 geometry via a natural divisibility of the circle into 6, 12, 24, and 360 parts, as shown in the arXiv paper. MATH: - Rational parametrization: \( t ↦ ( 1-t^2/1+t^2, 2t/1+t^2 ) \) — all rational points on \( x^2 + y^2 = 1 \) (excluding \((-1,0)\)). - Sexagesimal link: circle circumference divided by 6 gives chord length = radius (regular hexagon), leading to 360° = 6×60; 24 hours = 4×6; 12 months = 2×6. - Key ratios from the parametrization at special \( t \): - \( t = 1/2 \): point \( (3/5, 4/5) \) → Pythagorean triple, slope ratio 0.6/0.8 = 0.75. - \( t = 1/3 \): point \( (8/10, 6/10) = (4/5, 3/5) \) → reciprocal triple. - The tangent half-angle substitution \( t = tan(θ/2) \) yields \( sinθ = 2t/(1+t^2) \), \( cosθ = (1-t^2)/(1+t^2) \) — the core of Babylonian chord tables. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com