Ancient geometry find means Pythagoras’s number’s up

THE earliest known use of applied geometry has been identified – and it uses maths attributed to the Greek thinker Pythagoras 1,000 years later.

It was written on a tiny clay tablet that records the sale of a field in ancient Mesopotamia, modern-day Iraq.

Dating from 1900 to 1600BC, the tablet is thought to have been used by a surveyor to define land boundaries. On analysing the find, Daniel Mansfield, of the University of New South Wales in Australia, found the surveyor used ‘Pythagorean triples’. This involves drawing a triangle with sides that measure 3 units, 4 units and 5 units long.

A rectangle based on these measurements has mathematically perfect right angles – an important tool for ancient surveyors and one which is still used today. Dr Mansfield said: ‘The discovery and analysis of the tablet has important implications for the history of mathematics.

‘This is over a thousand years before Pythagoras was born. With this new tablet, we can actually see for the first time why they were interested in geometry: to lay down precise land boundaries. 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”.’

The tablet was found near Baghdad in 1894 but sat in a museum for more than 100 years without its significance being realised.

Born around 570BC, Pythagoras is credited with realising that the square of the hypotenuse, the side opposite a right angle in a triangle, is equal to the sum of the squares of the other sides. The formula is a² + b² = c².