Plimpton 322: Old Babylonian Secant-Squared Trigonometry Predates Greek Methods by 1000 Years — E8 Intelligence Research

FINDING: Old Babylonian tablet Plimpton 322 encodes a trigonometric table based on secant-squared values derived from normalized Pythagorean triples, predating Greek trigonometry by over 1000 years. MATH: - Key ratios: sec²(θ) = (c/b)², where (a,b,c) are Pythagorean triples with b as the short side. - Tablet rows correspond to angles from ~45° to ~30°, with sec² values decreasing from 2.000 to 1.387 (base-60: 2;00 to 1;23,13,46). - Underlying generator: p/q ratios (regular sexagesimal numbers) produce triples via a = p² - q², b = 2pq, c = p² + q². - Constant: 1.414 (√2) appears as sec(45°) = 1.414, encoded as 1;24,51,10 in base-60. CONNECTION: - Geometric harmony: sec² values map to unit circle rational points (x = b/c, y = a/c). The angles (θ) cluster near 45° (0.785 rad) and 30° (0.524 rad), linking to the golden ratio's complementary angles (e.g., 36° and 54°). - Base-60 system enables exact rational approximations of irrationals (e.g., √2 ≈ 1;24,51,10 = 30547/21600) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com