# Trigonometry on a 3700-year-old tablet from Babylon

Andrew Kelly/University of New South Wales The Plimpton 322 tablet contains cuneiform inscriptions with four columns and 15 rows of numbersAndrew Kelly/University of New South Wales

A 3700-year-old clay tablet from Babylon may be the oldest known record of concepts of trigonometry, the field of mathematics that studies relations between lengths of sides and angles of triangles. According to this interpretation, trigonometry may have begun in Mesopotamia about 1,000 years before it did in Ancient Greece. Daniel Mansfield and Norman Wildberger from the University of New South Wales in Australia defended this hypothesis by reanalyzing the cuneiform inscription on the Plimpton 322 tablet, now part of the Columbia University collection in New York (Historia Mathematica, August 24, 2017). Since the 1940s, some historians have suggested that the object contains a series of numbers similar to the Pythagorean theorem, according to which the square of a hypotenuse, the longest side of a right triangle, equals the sum of the squares of the other two sides. Now the two Australians have gone further in their interpretation of the object, comprised of four columns and 15 rows of numbers. They say that the table expresses the concepts of trigonometry using the base 60 form of mathematics, invented by the Sumers and later claimed by the Babylonians. “This is a whole different way of looking at trigonometry,” Mansfield told the journal Science. “We have to really get outside our own culture to see from their perspective to be able to understand it.” There were two different reactions to the rereading of the content of the clay object: some mathematicians praised the study, while others said it was speculative.

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