The Algorithm of Factor 12: Generating the Information Carved on the Plimpton 322 Tablet

Abstract

The right triangles represented in the Plimpton 322 data have integer sides $(a, b, d)$ with $a < b < d$, by inspecting the data we propose $b=M\,Q_{M}$ with $M,Q_{M}$ positive integers. In this way we present a new data-driven family of algorithms in order to generate the whole content of the Plimpton-322 tablet. Each algorithm of the family corresponds to one given value of the bundling factor or mak\c{s}arum $M$. The algorithm with $M=12$ arise naturally from data and is developed entirely through this work. We could generate the complete Plimpton 322 table by using three different schemes in the framework of the twelve factor algorithm. Finally we found by varying $M$ in the general algorithm, we can be able to find all the Pythagorean Triples.