Ancient Babylonian tablet contains oldest use of trigonometry

Prior to the new analysis, researchers had determined that the notations on the tablet displayed a particular numerical pattern of three positive integers, called Pythagorean triples.
By Chad Young | Aug 27, 2017
After spending two years analyzing a mysterious 3,700-year-old Babylonian clay tablet, researchers have concluded that it holds the oldest evidence ever found of a trigonometric table.

The study is published in the journal Historia Mathematica.

The tablet, dubbed Plimpton 322, was discovered in the early 1900s in what is now Iraq and suggests the Babylonians beat Greek astronomer Hipparchus of Nicaea (120-190 BCE) previously thought to have invented trigonometry by more a millennium.

Trigonometry is the study of the relationships between the angles and sides of triangles.

After the tablet was first discovered, an American antiquities buff named Edgar Banks bought it from a dealer. Banks worked as the American consul in Baghdad, but also was an amateur archaeologist who is believed to have inspired the famous film character Indiana Jones, a report by Live Science said.

Banks sensed the importance of the tablet and eventually sold it to New York publisher George Arthur Plimpton, with whom it remained until Plimpton's death in 1936. It was then donated to Columbia University, where it still resides.

Prior to the new analysis, researchers had determined that the notations on the tablet displayed a particular numerical pattern of three positive integers, called Pythagorean triples.

Because Babylonian mathematicians used a numerical system based on 60 instead of 10, the researchers used the 60-based system to show how the ancient scribes would have calculated the numbers pressed into the clay.

"The huge mystery, until now, was its purpose why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet," said co-author Daniel Mansfield said, in the Live Science report.

Using information from missing pieces of the tablet that had been reconstructed by other researchers, Mansfield and his colleague, mathematician Norman Wildberger, found that the original six columns of figures on the tablet represented a different type of trigonometry that used ratios rather than angles and circles.

"The tablet not only contains the world's oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry," Mansfield said.

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