Plimpton 322: Ancient Babylonian Sexagesimal Trigonometry Predates Greek Methods — E8 Intelligence Research

FINDING: Plimpton 322 is a 3700-year-old Babylonian clay tablet containing the world's first trigonometric table, based on base-60 (sexagesimal) arithmetic and exact ratios, not angles. MATH: The tablet lists 15 rows of Pythagorean triples (a² + b² = c²) in sexagesimal notation. Key constants: base-60 system (sexagesimal) uses 60 as radix, enabling exact fractions (e.g., 1/2 = 0;30, 1/3 = 0;20, 1/4 = 0;15). The triples are generated by a method equivalent to modern parameterization: a = p² - q², b = 2pq, c = p² + q², with p, q regular sexagesimal numbers (having only prime factors 2,3,5). The tablet's ratios (e.g., b²/(c² - b²)) correspond to sec²(θ) - 1 = tan²(θ), effectively a table of secant values. CONNECTION: Base-60 directly relates to geometric harmony: 60 = 2² × 3 × 5, enabling exact representation of fractions with denominators 2,3,4,5,6,10,12,15,20,30,60 — all divisors of 60. This aligns with the golden ratio's appearance in regular pentagons (5-fold symmetry) and the 60° a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com