Plimpton 322: A Sexagesimal Table of Decreasing Secant-Squared Values (45°–30°) — E8 Intelligence Research

Abstract

FINDING: Plimpton 322 encodes a decreasing sequence of secant-squared values (1/cos²θ) for angles 45° down to 30°, generated by reciprocal pairs in base-60. MATH: - Secant-squared values: \( \sec^2\theta = 1 + \tan^2\theta \), with \(\tan\theta = p/q\) from reciprocal pairs \((p, q)\) in sexagesimal. - Sequence: \(\sec^2\theta\) decreases from 2.0 (45°) to 1.333... (30°), corresponding to \(\theta\) from 45° to 30° in ~1° steps. - Key constants: \(\sqrt{2} \approx 1.4142\), \(\sqrt{3} \approx 1.732\), base-60 reciprocals (e.g., 2/1, 3/2, 4/3, ...). - Pythagorean triples: \(a = p^2 - q^2\), \(b = 2pq\), \(c = p^2 + q^2\), with \(c/a = \sec\theta\). CONNECTION: - Geometric harmony: The angle range 30°–45° spans the golden ratio's complementary angles (36°–54°), and sec² values relate to the golden ratio via \(\sec^2(36°) \approx 1.527\) and \(\sec^2(54°) \approx 1.236\). - Base-60: All entries are regular sexagesimal numbers (factors 2,3,5), linking to Babylonian lattice ar Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com