An ancient clay tablet dating back to 3,700 years has shown that the Babylonians knew the Pythagorean Theorem well over 1,000 years before the birth and popularity of the Greek philosopher Pythagoras.The ancient land surveyors used the Si.427 tablet to draw precise boundaries. It is engraved with cuneiform marks that form a mathematical table, which instructs the reader how to make right triangles. This tablet is the oldest known example of applied geometry.The tablet was first discovered by a French archeological expedition in 1894. It is currently kept in the Istanbul Archeological Museum.Researchers have only now discovered the significance of these ancient markings.Related: 11 Most Beautiful Mathematical Equations"It is generally accepted, that trigonometry, the branch of mathematics that deals with the study of angles, was developed by the ancient Greeks who studied the night sky," Daniel Mansfield, an Australian mathematician and discoverer of the meaning of the tablet, stated in a statement. "But, the Babylonians invented their own alternative called 'prototrigonometry' in order to solve problems related only to measuring the ground and not the sky.Mansfield claims that Si.427, the only example of an Old Babylonian cadastral document or a plan surveyor used to determine land boundaries, is Si.427. Mansfield stated that the document provides legal and geometric information about a field after it has been divided.The tablet shows a marshy area with several structures, including a tower built on top. Three sets of Pythagorean Triples are engraved on the tablet. These whole numbers are three that have the sum of squares from the first two and the square of third. Si.427 has three sets of triples: 3, 4, 5, 8, 15, 17, and 5, 12. These triples were probably used to determine the boundaries of the land.The significance of the tablet was not recognized for over 100 years. It was only then that it was finally tracked down. (Image credit UNSW SidneyAlthough the Pythagorean Theorem is not expressed on the tablet in the algebraic form it is used in today's, understanding the general principle that governs lengths of sides and hypotenuse would have been helpful.Mansfield discovered a tablet dating from 2017 called Plimpton 322, that he believed contained another trigonometric table. He was only able to see the triples on Si.427 to realize that ancient Babylonians used rudimentary trigonometric theories to divide up land parcels.Mansfield stated that Si.427 predates Plimpton 322 but may even have inspired it.There are many right triangles of different shapes. Babylonian surveyors can only use a small number of them. Plimpton 322 is an in-depth study of this zoo in order to find the useful shapes," Mansfield explained. He was referring to the fact different right triangle types can have different interior angles. This is a time when land became more private. People started to think about land as if it were their land. They wanted to create a boundary that would allow for positive neighbourly relations. This is exactly what the tablet says. It's a field that is being divided, and new boundaries are created."Mansfield says that although the reasons for the calculation of the land boundaries on the tablet weren't clear, Si.427 mentions a dispute over datepalms at the border between Sin-bel-apli, a prominent landowner, and a wealthy female landowner. He said that it was easy to see why accuracy was so important when resolving disputes among such powerful individuals.It would take 1,000 years between the creation and birth of Pythagoras, of Samos in the year 570 B.C. Therefore, the formalized Pythagorean rules are taught to students today. Experts have known for a long time that the Greeks inherited mathematical knowledge from Egyptians and the Egyptians in turn, from the Babylonians.Mansfield is surprised at the level of theoretical sophistication that the tablets reveal ancient Babylonians to possess at this early stage in human history.He said, "No one expected that the Babylonians would use Pythagorean Triples in this manner." It is closer to pure mathematics, inspired more by the practical problems at the time.Original publication on Live Science
