The oldest example of applied geometry was found on a 3700-year-old cuneiform tablet, which included so-called Pythagorean triples more than 1000 years before the Greek Pythagoras. The tablet was discovered by the Australian mathematician Daniel Mansfield in a museum in Istanbul, where it had been overlooked for more than 100 years. In the ancient Babylonian Empire, the cadastral document recorded legal and geometrical details of a field that was to be divided up after a sale.
Proto-trigonometry in Mesopotamia
The cuneiform tablet is called Si.427 and was excavated in 1894 in what is now Iraq near Baghdad. Their significance for the history of mathematics was only now recognized, explains the researcher from the University of New South Wales. The front side shows a schematic drawing of the field, which is divided by unexpectedly precise lines. The fact that the responsible surveyor managed to do this so precisely is due to the fact that he used the Pythagorean triples, i.e. natural numbers from which a right-angled triangle can be constructed. On the back, among other things, the size of the field is mentioned.
A few years ago, Mansfield discovered another cuneiform tablet, which is a unique trigonometric table, he explains. It is actually widely accepted in research that trigonometry – that part of geometry that deals with triangles – was developed in ancient Greece. That would have happened in the course of exploring the starry sky. However, both tables now show that a proto-trigonometry was created in the ancient Babylonian Empire 1000 years earlier to measure the ground.
Only the panel now being presented to the general public makes it clear why there was an interest in this early trigonometry at the time, and why it was about precise limits. In that epoch there was the first private land ownership and people wanted to have permanent markings on who owned what. Disputes that had to be settled by surveyors are also already mentioned on other boards. Mansfield now hopes to find further applications of Old Babylonian proto-trigonometry on cuneiform tablets, the importance of which has been overlooked so far. But Si.427 also poses a riddle to him: On the back there is a large “25.29”. He does not know what this is all about, he admits.