Plimpton 322's Sexagesimal Ratios: A Reconstruction Algorithm for Missing Pairs — E8 Intelligence Research

FINDING: Plimpton 322 encodes a systematic sequence of regular sexagesimal ratios (p/q) generating Pythagorean triples, with a reconstruction algorithm that accounts for "missing pairs" via a natural modification of Bruins' method. | MATH: The tablet lists 15 rows of (sexagesimal) values corresponding to triples (a, b, c) with a² + b² = c². Reconstruction uses regular numbers p, q in base 60 (i.e., p, q whose prime factors are only 2, 3, 5) to form ratios p/q. The standard parametrization: a = p² − q², b = 2pq, c = p² + q² (or scaled variants). Bruins' scheme: choose p, q from a regular sexagesimal grid; the "missing pairs" arise from gaps in the sequence where p/q falls outside the tablet's chosen interval (likely 1 < p/q < 1.5, with decreasing q). The arXiv paper (1109.3814v2) proposes a modified rule that predicts subsequent rows beyond row 15, implying a continuous, ordered algorithm — likely iterating p, q via multiplication by regular factors (e.g., 2, 3, 5) to maintain constant Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com