Trigonometry 1000 years before Pythagoras: Mathematician uncovers Mesopotamian secrets - Sydney Morning Herald

For more than a century, an unassuming ancient Mesopotamian clay tablet depicting a land sale has been lying in plain sight in an Istanbul museum.

Sydney mathematician Daniel Mansfield has now revealed the 3700-year-old artefact from the Old Babylonian period contains the earliest example of complex geometry in the world, in research published in Foundations of Science.

Dr Daniel Mansfield’s research shows the 3700-year-old artifact from the Old Babylonian period contains the earliest example of complex geometry in the world.Credit:UNSW

It shows trigonometry did not begin with the Greeks studying the sky but with the Babylonians surveying the ground.

“The discovery and analysis of the tablet have important implications for the history of mathematics,” Dr Mansfield, from the University of NSW, said.

“For instance, this is over a thousand years before Pythagoras was born.

“You’ve got trigonometry which is taught in schools, but now we’ve got this unexpected prequel where the Babylonians got there first.”

The tablet, known as Si.427, dates from the Old Babylonian period – 1900 to 1600 BCE – and Dr Mansfield discovered the land surveyor used a type of trigonometry that is now known as “Pythagorean triples” to make accurate right angles.

Dr Daniel Mansfield’s research shows the 3700-year-old artifact from the Old Babylonian period contains the earliest example of complex geometry in the world.Credit:UNSW

Si.427 gives legal and geometric details about a piece of land that was split and sold off, with a surveyor measuring out the new area and setting boundaries.

Dr Mansfield first heard about the unusual ancient clay tablet while reading records from an 1894 excavation in what’s now the Baghdad province in Iraq, before tracking it down in Turkey.

He was immediately amazed by the presence of perfect rectangles on the tablet.

“I’m thinking, how did they get them so perfect – how would you do that?” Dr Mansfield said.

In 2017, Dr Mansfield had speculated another artefact from the same period, known as Plimpton 322, was a unique kind of trigonometric table.

But he could only guess the purpose of the Plimpton 322, hypothesising that it had a practical use, possibly used to construct palaces and temples, build canals or survey fields.

“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 said.

“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.”

Dr Mansfield said the way these boundaries were made revealed people at the time had a real understanding at a theoretical level about the mathematics they were doing.

“Nobody expected that the Babylonians were using Pythagorean triples in this way,” Dr Mansfield said.

“It is more akin to pure mathematics, inspired by the practical problems of the time.

“It’s so unusual, no one from our modern approach to mathematics could have come up with something like this.”

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2021-08-04 15:00:02Z
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