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: \ (a² + b² = c²\) with integer sides. - Tablet lists columns: (a, c) pairs and a ratio \ (b²/ (c² - b²) \) or equivalent. - Base-60 representation: e. g. , row 1: a=119, c=169, b=120 → ratio \ (b²/ (c² - b²) = 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 \ (² () \) or \ (² () \) 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 \ (² () \) 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