Plimpton 322: A Sexagesimal Trigonometric Table of Exact Ratios — E8 Intelligence Research

FINDING: Plimpton 322 is a trigonometric table based on exact ratios (sexagesimal) rather than angles or circles, using normalized secant-like values for right triangles. MATH: The tablet lists 15 rows of Pythagorean triples (a, b, c) in sexagesimal, with b²/c² = (c² - a²)/c² = 1 - (a/c)². The key ratio is (b/c)², which is the square of the sine of the complementary angle. In modern terms, the table gives values of sec²(θ) = (c/b)², ranging from 1.9834 to 1.3872 (sexagesimal: 1;59,0,15 to 1;23,13,46). The generating formula: for coprime p > q, a = p² - q², b = 2pq, c = p² + q². The tablet uses normalized b/c ratios (i.e., 1/b * c), effectively a secant table. CONNECTION: The ratios (b/c)² correspond to 1 - (a/c)², and the descending order of these values mirrors a geometric progression of secant angles. The sexagesimal base (60) naturally yields exact fractions (e.g., 0;0,0,1 = 1/216000). The ratios 0.618, 1.618, 2.618 do not appear directly, but the underlying Pythagorean triples ge Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com