LONDON: The sale of a field in ancient Mesopotamia 3,700 years ago has been recognized as the first known use of applied geometry.

It was discovered that the surveyor of the land plot recorded the purchase on a clay tablet about the size of a palm by using complex strings of numbers known as Pythagorean triples.

“It’s a discovery that will completely change the way we view the history of mathematics,” said the lead researcher of the study, Dr. Daniel Mansfield of the University of New South Wales, Australia. “This is more than a thousand years before Pythagoras was born.”

Si.427, the label used by mathematicians to refer to the clay tablet, was first discovered near Baghdad in 1894, but it spent more than 100 years in a museum in Istanbul, left unnoticed by researchers. 

“It’s the only known example of a ‘cadastral’ document from the Old Babylonian period — a plan used by surveyors to define land boundaries,” Mansfield said.

“In this case, it tells us legal and geometric details about a field that was split after some of it was sold off.”

The Old Babylonian period lasted between about 1900 and 1600 BC, and saw the advancement of religious, literary and scientific works.

As a result of the Si.427 research, Mansfield believes that Babylonian surveyors would browse an array of Pythagorean triples and use one that best represented a rectangular plot to formulate a sales map, often using rope and other measuring devices.

“With this new tablet, we can actually see for the first time why they were interested in geometry: To lay down precise land boundaries,” Mansfield said.

“This is from a period where land started to become private. People started thinking in terms of ‘my land and your land,’ wanting to establish a proper boundary to have positive neighborly relationships. And this is what this tablet immediately says. It’s a field being split and new boundaries being made.”