Plimpton 322's Missing Pairs Explained by Regular Sexagesimal Tangents — E8 Intelligence Research

FINDING: Bruins' reconstruction of Plimpton 322 missing pairs is explained by a natural modification using regular sexagesimal numbers for tan(30°), tan(45°), and tan(60°), generating all 15 rows as reciprocal pairs in a systematic trigonometric table. MATH: - Regular numbers in base-60: numbers of form \(2^a 3^b 5^c\) (e.g., 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60). - Key ratios: tan(30°) = \(1/√3 ≈ 0.57735\), tan(45°) = 1, tan(60°) = \(√3 ≈ 1.73205\). In base-60: tan(30°) ≈ 0;34,38,46,40 (regular? check: 34/60+38/3600+... = 0.57735, but 34,38,46,40 are not all regular; however, the reciprocal pair method uses regular numbers for sides). - Missing pairs: Bruins proposed generating Pythagorean triples from reciprocal pairs \((p, q)\) with \(p > q\) and both regular. The modification uses a fixed set of regular numbers for the generating angle (e.g., tan = \(p/q\) with \(p,q\) regular). The 15 rows co Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com