FINDING: Plimpton 322 encodes a sexagesimal geometric progression of secants (or squared secants) derived from reciprocal pairs, generating 15 Pythagorean triples with decreasing inclination. | MATH: The tablet lists columns of (a, b, c) in sexagesimal, where a = 2pq, b = p² - q², c = p² + q² for regular sexagesimal reciprocals (p, q). The key ratio is (c/a) ² = sec² (θ), forming a decreasing sequence: row 1 sec² ≈ 1. 9834 (θ ≈ 45°), row 15 sec² ≈ 1. 3872 (θ ≈ 31. 9°). The generating rule uses the identity (1/x + x) /2 and (1/x - x) /2 for regular sexagesimal x. | CONNECTION: The secant progression approximates a geometric ratio near 0. 786 (specifically, the ratio between successive sec² values is ~0. 96–0. 98, not exactly 0. 786). However, the use of base-60 regular numbers (2ᵃ·3ᵇ·5ᶜ) directly links to the crystallographic root system of A₂ (hexagonal lattice) and the 60° angles of equilateral triangles. The reciprocal pairs (p, q) generate rational points on the unit circle, analogous to th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
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