UNSW solves mathematical mystery

Dominica Sanda

Scientists at a university in Sydney have solved a mystery that's had mathematicians around the world scratching their heads for more than 70 years.

Since the discovery of the famous 3700-year old Babylonian clay tablet, known as 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 scientists have cracked the code, revealing it was possibly used by ancient mathematical scribes to calculate how to construct palaces and 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," Dr Daniel Mansfield of the School of Mathematics and Statistics in the UNSW Faculty of Science said in a statement on Friday.

"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."

Its use of ratio-based trigonometry rather than trigonometry based on angles and circles makes it the world's most accurate trigonometric table, Dr Mansfield says.

"It is a fascinating mathematical work that demonstrates undoubted genius," he said.

It took two years for Dr Mansfield and UNSW associate professor Norman Wildberger to come up with the theory, and now they're calling on scientists to test it.

"I doubt we have nailed it, I want people to go out and test and criticise it and make it better through analysis and debate," Dr Mansfield told AAP on Friday.

It also 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.

The tablet has been dated to between 1822-1762 BC and sits in the Rare Book and Manuscript Library at Columbia University in New York.