Plimpton 322: Babylonian Trigonometry Predates Greek Methods by 1,000 Years — E8 Intelligence Research

FINDING: Plimpton 322 is a 3800-year-old Babylonian clay tablet containing a precise trigonometric table based on Pythagorean triples, predating Greek trigonometry by over 1000 years and using a base-60 (sexagesimal) system for exact ratios. MATH: The tablet lists 15 rows of Pythagorean triples (a, b, c) satisfying a² + b² = c², with a/b ratios decreasing in regular steps. Key constants emerge from the sexagesimal fractions: the ratios correspond to sec²(θ) values (c/b)², ranging from 1.9834 to 1.3872. The underlying generating formula is: a = 2pq, b = p² - q², c = p² + q², where p and q are regular sexagesimal numbers (having only 2, 3, 5 as prime factors). The tablet uses exact fractions, not approximations, with ratios like 1.4142 (√2) and 1.7321 (√3) encoded in base-60. CONNECTION: The sexagesimal base-60 system directly links to geometric harmony: 60 is divisible by 2, 3, 5, producing ratios 0.5, 0.333, 0.2, and their reciprocals 2, 3, 5. The Pythagorean triples generate the gol Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com