Lying in plain sight, clay tablet revealed as oldest example of complex geometry

© UNSW Sydney

There it was, nestled snuggly at the Istanbul Archaeological Museum for over 100 years after it was unearthed in the 19th century in the ancient Babylonian city Sippar (present-day Iraq). Who knew what secrets the artefact had kept all these years? According to research published in the journal ‘Foundations of Science’, the clay tablet known as Si.427 contains the earliest example of complex geometry. Dating back 3 700 years, the hand tablet was created by a Babylonian surveyor who wrote on it with a stylus.

Altering the history of mathematics?

Judging by the time period, the Babylonians were using Pythagorean ideas long before the Greek philosopher Pythagoras. Apparently, trigonometry didn’t begin up there in the sky with the Greeks, but with the Babylonians down on the ground. “The discovery and analysis of the tablet have important implications for the history of mathematics,” commented lead researcher Dr Daniel Mansfield from the University of New South Wales in Australia in a news release. “For instance, this is over a thousand years before Pythagoras was born.” The land surveyor applied advanced mathematics to make boundary lines. Specifically, he used a type of trigonometry now known as Pythagorean triples to create accurate right angles. It marks the first time Babylonians used theoretical understanding of geometry to work out practical problems. They were way ahead of their time.

All about a piece of land that’s being sold

“Si.427 dates from the Old Babylonian (OB) period – 1900 to 1600 BCE,” explained Dr Mansfield. “It’s the only known example of a cadastral document from the OB period, which is a plan used by surveyors to define land boundaries. In this case, it tells us legal and geometric details about a field that’s split after some of it was sold off.” “With this new tablet, we can actually see for the first time why they were interested in geometry: to lay down precise land boundaries,” Dr Mansfield added. “This is from a period where land is starting to become private – people started thinking about land in terms of ‘my land and your land’, wanting to establish a proper boundary to have positive neighbourly relationships. And this is what this tablet immediately says. It’s a field being split, and new boundaries are made.” “Much like we would today, you’ve got private individuals trying to figure out where their land boundaries are, and the surveyor comes out but instead of using a piece of GPS equipment, they use Pythagorean triples,” Dr Mansfield told ‘The Guardian’. “Once you understand what Pythagorean triples are, your society has reached a particular level of mathematical sophistication.” “Now that we know what problem the Babylonians were solving, that recolours all the mathematical tablets from this period,” concluded Dr Mansfield. “You see mathematics being developed to address the needs of the time.”

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