3,700-Year-Old Tablet Shows The Oldest Known Example of Applied Geometry

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A mathematician has discovered that a 3,700-year-old clay tablet created by ancient Babylonians is the oldest example ever found of applied geometry.

The discovery is outlined in a new scientific paper regarding the tablet known as Si.427 or Plimpton 322. The realisation that the tablet was related to mathematics was first made in 2017 but it is only now that the details have been decoded.

Daniel Mansfield of the University of New South Wales (UNSW) in Australia, who made the discovery, told reporters:

“Si.427 dates from the Old Babylonian (OB) period – 1900 to 1600 BCE. 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.”

The Babylonian model uses the unique base number 60, which is significantly different to our modern knowledge of geometry and trigonometry, as first formulated by Ancient Greek Pythagoras.

Mansfield said:
“This raises a very particular issue – their unique base 60 number system means that only some Pythagorean shapes can be used. It seems that the author of Plimpton 322 went through all these Pythagorean shapes to find these useful ones. This deep and highly numerical understanding of the practical use of rectangles earns the name ‘proto-trigonometry’ but it is completely different to our modern trigonometry involving sin, cos, and tan.”

He also added the historical and social significance of such a device, saying:

“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. Nobody expected that the Babylonians were using Pythagorean triples in this way. It is more akin to pure mathematics, inspired by the practical problems of the time.”

While the mathematics used is not as complex as that created or discovered by the Ancient Greeks, it does show that ancient peoples had a profound understanding of the relationship between their daily lives and mathematics.

[h/t: Science Alert]

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