Plimpton 322's Genesis: A Modified Bruins Reconstruction for Missing Pairs — E8 Intelligence Research

FINDING: The search results are dominated by generic numerical-methods tutorials (spline, Newton forward, Vandermonde, IK solvers) — none of which address Plimpton 322 or ancient secant tables. The sole relevant item is an arXiv paper on Plimpton 322's genesis, which proposes a modified Bruins reconstruction to account for "missing pairs" and predicts subsequent entries. MATH: The paper (arXiv:1109.3814v2) does not provide explicit equations in the snippet. However, the standard Plimpton 322 mathematical content is: 15 rows of Pythagorean triples (a, b, c) with b² = c² − a², expressed in sexagesimal. The ratios b/c and a/c correspond to secant and tangent values. Bruins' original method uses reciprocal pairs (x, 1/x) from regular sexagesimal numbers, generating triples via: a = (x − 1/x)/2, b = (x + 1/x)/2, c = 1 (or scaled). The "missing pairs" refer to regular numbers skipped between consecutive rows. The paper's modification likely uses a systematic angular spacing — but the sn Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com