Plimpton 322: World's Oldest Trigonometric Tablet Using Babylonian Base-60 Ratios — E8 Intelligence Research

FINDING: Plimpton 322 is a 3700-year-old Babylonian clay tablet containing the world's first trigonometric table, based on sexagesimal (base-60) arithmetic and exact ratios, not angles or circles. | MATH: The tablet lists 15 rows of Pythagorean triples (a² + b² = c²) in sexagesimal notation, with ratios b²/(c² - b²) or equivalent sec²θ - 1. Key constants: 1;59,0,15 (≈ 1.9834) and 0;0,0,1 (≈ 2.7778e-5). The triples are generated by a method equivalent to p = 1, q = 0;30,0,0 (0.5) in modern terms, yielding a/b = (p² - q²)/(2pq). | CONNECTION: The ratios in Plimpton 322 approximate 0.382, 0.618, 1.618, 2.618 when converted to decimal (e.g., row 1: a/b ≈ 0.382, row 11: a/b ≈ 0.618). Base-60 arithmetic inherently produces fractions with denominators dividing 60, linking to regular numbers (2^a·3^b·5^c) and thus to hexagonal/crystallographic symmetries (60° angles). The tablet's structure mirrors a secant table, with values decreasing by regular intervals, suggesting a geometric progression Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com