The numbers behind Plimpton 322

TL;DR

This paper offers a natural mathematical and cultural reinterpretation of the Plimpton 322 tablet, improving the explanation of its number patterns and predicting additional rows, thus enhancing understanding of Old Babylonian mathematics.

Contribution

It introduces a modified explanation for Plimpton 322's numbers that accounts for missing pairs and predicts new data, extending prior reconstructions.

Findings

Provides an economical account for missing pairs in Plimpton 322

Predicts five new rows extending the known content of the tablet

Enhances understanding of Old Babylonian mathematical practices

Abstract

A mathematically and culturally natural modification of Evart Bruins' explanation of the genesis of the numbers on the Old Babylonian tablet Plimpton 322 gives an economical accounting for the "missing pairs" in his reconstruction. When the new scheme is used to predict the numbers that would follow those on Plimpton 322, the results add five new rows to those listed by Price and Friberg in their hypothetical extension of the content of Plimpton 322 to rows covering the edges and back.