Table of whole-number sides of Pythagorean triangles

Plimpton 322 (obverse)

Plimpton 322 (obverse).
Image by Christine Proust. All rights reserved.

Plimpton 322 (reverse)

Plimpton 322 (reverse).
Image by Christine Proust. All rights reserved.

Columbia University Plimpton 322

Old Babylonian Period (19th-17th century BCE), Larsa?
Acquired 1922/1923 by George Plimpton, and given to Columbia in 1936

The most renowned of all mathematical cuneiform tablets since it was published in 1945, Plimpton 322 reveals that the Babylonians discovered a method of finding Pythagorean triples, that is, sets of three whole numbers such that the square of one of them is the sum of the squares of the other two. By Pythagoras' Theorem, a triangle whose three sides are proportional to a Pythagorean triple is a right-angled triangle. Right-angled triangles with sides proportional to the simplest Pythagorean triples turn up frequently in Babylonian problem texts; but if this tablet had not come to light, we would have had no reason to suspect that a general method capable of generating an unlimited number of distinct Pythagorean triples was known a millennium and a half before Euclid.

Plimpton 322 has excited much debate centering on two questions. First, what was the method by which the numbers in the table were calculated? And secondly, what were the purpose and the intellectual context of the tablet? At present there is no agreement among scholars about whether this was a document connected with scribal education, like the majority of Old Babylonian mathematical tablets, or part of a research project.