than modern mathematicians
The Babylonian clay tablet, created 3,700 years ago, contains a more accurate trigonometric table than those used by modern mathematicians today.
This artifact belonged to the American diplomat and collector of antiquities Edgar Banks. Today this man is better known as the prototype of Indiana Jones, the hero of the series of adventure films, who is brilliantly played by the cult Hollywood actor Harrison Ford.
In 1898, Banks took over as the American consul in Baghdad and, in addition to serving, was engaged in the fact that hundreds of ancient cuneiform clay tablets bought from "black diggers" and resold them to museums. The clay tablet, which became a real scientific sensation, was sold by Banks to New York publisher George Plimpton in 1922 for only $ 10.
This was the 322th tablet in the Plymton collection, so it was named Plympton 322. After the publisher's death, the collection was donated to Columbia University.
Scientists have named this tablet one of the most unique mathematical artifacts in the world. After deciphering the cuneiform signs, it turned out that a sequence of Pythagorean triplets was written on the clay.
What it is? You probably remember from the school mathematics course the expression "Pythagorean pants are equal in all directions"? So, Pythagorean triples is an ordered set of three natural numbers (x, y, z), which correspond to the lengths of the sides of a right-angled triangle. Moreover, they must satisfy the quadratic equation x2 + y2 = z2 from the Pythagorean theorem.
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Recall that the theorem says: the sum of the squares of the legs is equal to the square of the length of the hypotenuse. Just a small trifle - this tablet was written by the Sumerians, at least 1000 years before the birth of Pythagoras.
For a long time, scientists could not come to a consensus: for what purpose did this tablet serve? The matter was further complicated by the fact that the left part of the plate was chipped off and the historians had an incomplete text in their hands. For a long time it was believed that it was a manual for teachers of mathematics. Allegedly, using this "cheat sheet", the teachers checked whether the children solved the quadratic equations correctly.
However, mathematicians Daniel Mansfield and Norman Wildberger from the University of New South Wales (Australia) argue that this artifact has nothing to do with children's fun.
“In fact, this is a trigonometric table based on a method completely unknown to us, which was 3000 years ahead of its time,” says Professor Mansfield. - Plympton 322 is a powerful computational tool used for architectural calculations in the construction of palaces, temples, stepped pyramids, laying canals and accurately determining the boundaries of land holdings.
Australian mathematicians argue that the trigonometric table of the ancient Babylonians allows for more accurate calculations. The fact is that they used not a decimal, but a sixty-decimal number system. Now we only use this system to measure time (1 hour consists of 60 minutes, and a minute consists of 60 seconds) and angles (for example, a circular panorama around you is divided into 360 degrees).
The old Babylonian system is better suited for accurate trigonometric calculations, since the modern decimal system allows too much error. Relatively speaking, in the decimal system, you cannot completely divide the base number 10 by 3 or 4. The exact value you get when dividing 10 only by 5 and 2. And the hexadecimal calculus allows you to divide the base unit without a remainder - 60, by a much larger number fragments.
“I don’t remember the times when the ancients could teach the modern world something new,” says Daniel Mansfield. - Plympton-322 is the only fully accurate trigonometric table in the world today, it surpasses modern trigonometry. After 3,000 years, Babylonian mathematics may be back in vogue. It has great potential for use in geodetic work or for solving computer graphics problems.
For a long time, the ancient Greek scientist Hipparchus was called the father of trigonometry. He lived in the second century BC and was the first to compile an analogue of modern tables of trigonometric functions. However, it turns out that the Babylonians had much more accurate mathematical knowledge 1500 years before Hipparchus. It is a pity that we will never know the names of the Sumerian perelmans.
DOSSIER
Plympton 322 is a tablet from the Sumerian city of Larsa, which was written around 1800 BC. e. By this time, the city was conquered by the Babylonian kingdom and lost its independence. The obverse of the artifact depicts a table consisting of 15 lines and 4 columns filled with cuneiform characters. It is made of clay and measures 12.7 cm by 8.8 cm. The left side of the artifact is broken off, but scientists have established that in the original the full text of the trigonometric table contained 6 columns and 38 lines.
YAROSLAV KOROBATOV