An ancient clay tablet proves that trigonometry was known in Mesopotamia at the time of Hammurabi

Trigonometry , in its classical definition, is a branch of mathematics where trigonometric functions are studied, as well as their use in geometry. The term “trigonometry” appeared in 1565 thanks to the mathematician Bartolomeus Pitiskus, whose book was called “Trigonometry”. The basics of trigonometry were used not only in the Middle Ages, this science was also known to ancient scientists who performed complex calculations in astronomy, architecture, geodesy, etc.

It was believed that the first trigonometry for various purposes (astronomy, construction) began to be used by scientists of Ancient Greece. But now there is evidence that the Babylonians were the first to live, one and a half thousand years earlier than the ancient Greek astronomer Hipparchus. He is considered the father of trigonometry, since he created the first trigonometric tables that have survived to this day.

The civilization of the Tigris and Euphrates is one of the oldest on Earth. The Babylonians had all the signs of a high civilization - writing (as many as two thousand characters), cities, and large enough, and money. Of course, there were crafts, agriculture and architecture, very complex for that time. Mesopotamia was already civilized one and a half thousand years before the foundation of Rome.

As for architecture, it was here that the Babylonians most likely worked with trigonometry. An indirect proof of this can be a clay tablet codenamed Plimpton 322. It was discovered by Edgar Banks at the very beginning of the 20th century (incidentally, the image of Indiana Jones was written from it). It is believed that the tablet was created in the years 1822-1762 BC. It was then that in Babylon Hammurabi ruled , which gave Mesopotamia a lot.



On the plate are written 15 lines of numbers, which are Pythagorean triples. So called numbers that satisfy the condition x ^ 2 + y ^ 2 = z ^ 2. According to the Pythagorean theorem, these numbers describe the lengths of the sides of a right triangle.

Previously, it was believed that this tablet was used at the school, and the teacher used it to check students' answers. But this year, a more original opinion appeared, expressed by scientists Daniel Mansfield and Norman Wildberger from the University of New South Wales in Australia. They believe that the table, drawn on clay, was used either to teach trigonometry (not to schoolchildren, but already to "students"), or to solve architectural problems during the creation of various buildings.


As it turned out, the numbers in the table describe a certain sequence of 15 right-angled triangles, where the inclination of the hypotenuse changes from one figure to another. According to the Australians, the plate originally had 38 figures. It is likely that it is so, since the left edge is broken off. By the way, the fact that the plate depicts numbers related to the Pythagorean theorem, scientists found out only in the 1940s.

Unfortunately, the belonging of the table to sculptors or scholars of antiquity is only an assumption. There are no facts that directly indicate that this clay tablet was used by ancient architects or mathematicians. Nevertheless, the Australians insist that with the help of this tablet (and possibly many others) the Babylonians built palaces, temples, canals. It may well be that the same hanging gardens were built with the participation of ancient mathematicians, well versed in trigonometry.

Mathematician historian Christine Proust of the French National Center for Scientific Research in Paris claims that the real purpose of the tablet is unknown. So the question of what it is and what it was used for remains open. Whatever it was, but this artifact confirms the high level of science and culture in Mesopotamia. This civilization is one of the greatest in history.

Thanks to other preserved tablets and other artifacts of Babylon, we know that at that time the calculating technique was more perfect than the Egyptian one. The Babylonians were able to solve quadratic equations, geometric progressions, then proportions, arithmetic means, percentages were used. By the way, a few years ago on Geektimes was published An interesting article on mathematics in Ancient Babylon.