# 3,700-Year-Old Babylonian Tablet Decoded

Plympton 322 is a famous Babylonian clay tablet showing numbers that can form the sides of right-angled triangles. UNSW/Andrew Kelly

Almost a century ago, Edgar Banks – the inspiration for Indiana Jones – dug up a clay tablet in southern Iraq, but it took until now for its meaning to be understood. With this explanation has come insight into Babylonian mathematics, which operated on a different, and in some ways preferable, system than our own.

In 1945, it was realized that the tablet, known as Plimpton 322 after it was sold to collector George Plimpton for \$10, had mathematical significance, but the details remained a mystery. New research argues it represents part of a trigonometric table, and one more accurate than those that came afterwards.

Plimpton 322's burial location in what was once the city of Larsa indicates it's 3,700 years old, dating from the time of Hammurabi, who established one the earliest surviving legal codes. “Plimpton 322 has puzzled mathematicians for more than 70 years, since it was realized it contains a special pattern of numbers called Pythagorean triples,” said Dr Daniel Mansfield of the University of New South Wales in a statement. Pythagorean triples are any whole numbers a, b, and c that can form a right-angle triangle through the formula a2 + b2 = c2, with 3, 4, and 5 being the most familiar example.

“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,” Mansfield continued.

Mansfield became interested in the problem and collaborated with his colleague Dr Norman Wildberger to try to unravel it. Wildberger is the inventor of a new way of doing trigonometry, based on the ratio of sides rather than angles. In 2005, he published a book, Divine Proportions: Rational Trigonometry to Universal Geometry, demonstrating that any problem that can be solved using traditional trigonometric methods canalso  be solved using his technique, and often more easily for those who have taken the time to learn it.

The idea of Plimpton 322 as a trigonometric table had been raised before, and eventually rejected, but this was done in the absence of an understanding of Wildberger's methods.