MERLIN SCIENCE — Plimpton 322 as Rank-3 Lattice of Reciprocal-Pair Pythagorean Triples — E8 Intelligence Research

The finding is this: Plimpton 322 encodes fifteen Pythagorean triples generated by reciprocal pairs of regular sexagesimal numbers, and the whole tablet is best understood as a rank-three lattice problem embedded in the Babylonian metrological system. If you work with number theory or the history of mathematics, you know the standard reading. Plimpton 322 is usually treated as a trigonometric table, or a teacher's list of solved problems, or a scratch pad. What that framing misses is the generative structure underneath. The scribes weren't listing triples. They were computing them from a parameterization, and the parameters they chose tell us what they actually understood. Here is the mechanism, and you can check every step. Take two regular sexagesimal numbers, p and q, meaning their only prime factors are 2, 3, and 5. Form the short side as p squared minus q squared, the diagonal as p squared plus q squared, and the middle side as 2pq. Column one tabulates c over a squared, which i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com