Plimpton 322: An Old Babylonian Sexagesimal Trigonometric Table of Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 is an Old Babylonian table of 15 rows of Pythagorean triples, likely representing a primitive trigonometric table based on ratios (sexagesimal) rather than angles. MATH: - Pythagorean triples: \(a^2 + b^2 = c^2\) (with a < b). - Sexagesimal (base-60) entries: e.g., row 1 gives (119, 120, 169) → ratio \(b/a = 120/119 ≈ 1.0084\), \(c/a = 169/119 ≈ 1.420\). - Key ratios extracted: \(b/a\) and \(c/a\) correspond to secant and tangent in modern terms. - No explicit trigonometric functions, but the tablet lists pairs \((b/a, c/a)\) for 15 decreasing values of \(b/a\) from ~1.008 to ~0.383. CONNECTION: - The ratio \(b/a\) ranges from ~1.008 down to ~0.383, which is close to the golden ratio conjugate \(0.382\) (1/φ²). This suggests a systematic progression toward a harmonic limit. - Base-60 mathematics aligns with 60-fold symmetry (hexagonal/crystallographic) and 360° circles. - The triples themselves are integer solutions to \(a^2 + b^2 = c^2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com