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

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: \( ^2θ = 1 + tan^2θ \), with \(tanθ = p/q\) from reciprocal pairs \((p, q)\) in sexagesimal. - Sequence: \(^2θ\) decreases from 2.0 (45°) to 1.333... (30°), corresponding to \(θ\) from 45° to 30° in ~1° steps. - Key constants: \(√2 ≈ 1.4142\), \(√3 ≈ 1.732\), 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 \(c/a = θ\). 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 \(^2(36°) ≈ 1.527\) and \(^2(54°) ≈ 1.236\). - 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