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The World’s Oldest and Most Accurate Trigonometry Table

Daniel Mansfield holds the Plimpton 322 tablet at the Rare Book and Manuscript Library at Columbia University in New York. Credit: Andrew Kelly/UNSW

Daniel Mansfield holds the Plimpton 322 tablet at the Rare Book and Manuscript Library at Columbia University in New York. Credit: Andrew Kelly/UNSW

By Daniel Mansfield

By decoding an ancient stone tablet, researchers have realised that the Babylonians employed a form of trigonometry that is very different to our own.

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Plimpton 322 is one of the most famous tablets from the Old Babylonian period (19th–16th century BCE). It was obtained, perhaps illegally, in the southern Iraq desert where it found its way into the hands of Edgar Banks (the inspiration for the fictional character Indiana Jones).

In about 1922 Banks sold the tablet to the famous publisher and antiquities collector George Arthur Plimpton. Shortly before his death, Plimpton bequeathed his entire collection to the University of Columbia, where the artefact known as “Plimpton 322” remains today.

The tablet itself contains a fragment of a larger table: four columns with headings, and 15 rows of numbers remain. Neither Banks nor Plimpton knew any more than that. In 1945 the surviving column headings were translated, and the numbers were revealed to describe the sides of right triangle of steadily decreasing slope, along with a squared ratio of sides.

This presented quite a conundrum: angles and trigonometry as we know it would not be invented for another 1500 years, and yet this appears to be some kind of trigonometric table. The answer, which was recently published in Historia Mathematica, is that the Babylonians had a form of trigonometry that was so very different to our own that it has taken us more than 70 years just to recognise it.

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The full text of this article can be purchased from Informit.