Plimpton 322: A Sexagesimal Table of Secant Squares and Pythagorean Triples — E8 Intelligence Research

FINDING: Plimpton 322 encodes a sexagesimal geometric progression of secant squares (or squared ratios) corresponding to a decreasing sequence of generating angles, forming a primitive Pythagorean triple table with a hidden trigonometric structure. MATH: Each row yields a normalized right triangle with short side \(a\), long side \(b\), and diagonal \(d\) such that \(a^2 + b^2 = d^2\). The tablet lists \(d^2 / a^2\) (secant squared) in sexagesimal, decreasing linearly from row 1 to row 15. The generating parameter \(p/q\) (with \(p > q\), both regular sexagesimal integers) produces triples via \(a = p^2 - q^2\), \(b = 2pq\), \(d = p^2 + q^2\). The secant ratio \(d/a = (p^2+q^2)/(p^2-q^2)\) yields values: row 1 ≈ 1.9834 (sexagesimal 1;59,0,15), row 15 ≈ 1.3872 (sexagesimal 1;23,13,46). The step between successive secant squares is approximately constant in reciprocal form, suggesting a geometric progression of angles. CONNECTION: The secant values correspond to angles \(θ\) whe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com