Plimpton 322: A Sexagesimal Table of Secant-Squared Ratios for Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic method for generating Pythagorean triples using base-60 (sexagesimal) ratios, specifically secant-squared (sec²) values as regular numbers in a tabular form. | MATH: For a right triangle with sides a, b, c (a < b < c), the tablet lists pairs (b, c) such that (c/b)² = 1 + (a/b)². The preserved columns correspond to: Column I: (c/b)² = sec²(θ) (where θ is the angle opposite side a). Column II: b (short side). Column III: c (hypotenuse). The ratios are given in sexagesimal, e.g., row 1: (c/b)² = 1.9834027... (base-60: 1;59,0,15). The generating method uses reciprocal pairs (p, q) with p > q, both regular in base-60, to produce triples: a = p² - q², b = 2pq, c = p² + q². The tablet selects only those where (c/b)² is a regular sexagesimal number (i.e., finite base-60 expansion). | CONNECTION: The ratios (c/b)² cluster near 1.9834, 1.9492, 1.9188, ... which correspond to angles θ ≈ 45° to 30°. The reciprocal pairs (p, q) are chosen such that p/q ≈ √ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com