Plimpton 322: Babylonian Exact Rational Trigonometry via Sexagesimal Reciprocal Pairs — E8 Intelligence Research

FINDING: Plimpton 322 encodes 15 Pythagorean triples generated by sexagesimal reciprocal pairs (t-values), revealing Babylonian mastery of exact rational trigonometry and regular number factorization. | MATH: The tablet's columns correspond to (c/a)² and (b/a)² for triples (a,b,c) with a²+b²=c². In base-60, entries derive from t = p/q (regular sexagesimal fractions, i.e., q = 2^α·3^β·5^γ). Standard reconstruction: a = 2t/(1+t²), b = (1−t²)/(1+t²), c = (1+t²)/(1+t²) — but normalized to a=1 gives b/a = (1−t²)/(2t), c/a = (1+t²)/(2t). The tablet's t-values are regular: e.g., t = 12/5, 64/27, 75/32, 125/54, etc., yielding exact sexagesimal reciprocals. Key ratios: row 1 gives c/a = 169/120 ≈ 1.4083, b/a = 119/120 ≈ 0.9917; row 5 gives c/a = 1.785, b/a = 1.48. The diagonal ratios (c/b) range from ~1.42 to ~1.99. | CONNECTION: The t-values are precisely the tangent half-angle parameters: t = tan(θ/2). Thus b/a = cot(θ) and c/a = csc(θ) — a full rational trigonometry in base-60. The regular n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com