Scientists at a university in Sydney have cracked a mystery that has had mathematicians around the world scratching their heads for the better part of a century.

Since the discovery of the famous 3700-year-old Babylonian clay tablet, Plimpton 322, in the early 1900s in southern Iraq, mystery has surrounded what the ‘triangular’ code was used for.

But University of New South Wales (UNSW) scientists have cracked the code, revealing it was possibly used by ancient mathematical scribes to calculate how to construct palaces, temples, and build canals.

“Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realised it contains a special pattern of numbers called Pythagorean triples,” said Dr. Daniel Mansfield of UNSW.

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.

Dr. Mansfield came across prior research on the tablet “purely by chance” while looking for classroom material. Like other mathematicians, he recognised it as likely to be some sort of trigonometry but couldn’t figure out how.

The key came with the help of a colleague, Professor Norman Wildberger, who had previously worked extensively on trigonometry based on ratios, rather than angles and circles like we currently understand.

“Once we looked at it in a different way, it all fell into place,” Dr. Mansfield said.

Its use of ratio-based trigonometry rather than trigonometry based on angles makes it the world’s most accurate trigonometric table, according to Dr. Mansfield.

“This provides a new way of looking at trigonometry,” he said. “That’s the valuable part.”

It reveals the Babylonians, not the Greeks, were the first to study trigonometry—the study of triangles—and opens up new possibilities for modern mathematics research and education.

“With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own,” Prof. Wildberger noted.

It took two years for Dr. Mansfield and Professor Wildberger to develop the theory, and now they are calling on scientists to test and criticize it to refine their findings. The tablet is dated between 1822–1762 BC and sits in the Rare Book and Manuscript Library at Columbia University in New York.