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An ancient clay tablet shows that Babylonian scholars might have invented trigonometry

An ancient clay tablet shows that Babylonian scholars might have invented trigonometry


This form of trigonometry is very different from what is currently used

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Image: UNSW/ Andrew Kelly

A new interpretation into the nature of an ancient clay tablet known as Plimpton 322 claims that ancient Babylonians might have developed an advanced form of trigonometry — long before Greek mathematicians are commonly believed to have invented the concept.

That’s the theory put forward by two mathematicians from the University of New South Wales, Daniel F. Mansfield and Norman Wildberger, who published their study in the latest issue of Historia Mathematica. They claim that the tablet demonstrates a sophisticated understanding of mathematics, and that modern assumptions of the field should be reexamined in light of the interpretation.

The tablet in question is approximately five inches wide by three inch tall, and dates back to somewhere between 1822 and 1762 BCE. It was discovered by an American archeologist and diplomat named Edgar Banks in Larsa (what is now in southern Iraq) in the early 1920s. Banks sold the tablet to New York publisher George Arthur Plimpton, who later bequeathed it and his collection to Columbia University.

The tablet contains four columns and 15 rows of cuneiform numbers, which conform to the Pythagorean theorem — the relationship between three sides of a right triangle. Over the years, researchers have theorized that the tablet was evidence of the use of trigonometry, while others have suggested that the tablet might have been mathematical exercises used by a teacher. This new study claims that the tablet could be evidence “of a completely unfamiliar kind and was ahead of its time by thousands of years.”

Mansfield and Wildberger say that if their interpretation is correct, Plimpton 322 would not only be the oldest known trigonometric table, but it would also be the “world’s only completely accurate trigonometric table.” The study’s authors note that this form of trigonometry is different from what’s used today: it wouldn’t use angles or approximations, because that base-60 system would allow mathematicians to use whole numbers, leading to exact calculations, which in turn would be useful for constructing fields, canals, or buildings.

The theory is not without some criticism, according to Science. Historian Mathieu Ossendrijver of Humboldt University in Berlin notes that there’s no proof that the Babylonians used this tablet for construction, while mathematical historian Christine Proust of the French National Center for Scientific Research in Paris says that while the idea makes sense, it’s “highly speculative.”