An artifact from ancient Babylon contains a more accurate trigonometric table than that of modern mathematicians

The Babylonian clay tablet, created 3700 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 a series of adventure films, which is brilliantly played by the cult Hollywood actor Harrison Ford.
In 1898, Banks took over as US consul in Baghdad and, in addition to the service, was engaged in the fact that he bought hundreds of ancient cuneiform clay tablets from "black diggers" and resold them to museums. The clay tablet, which became a real scientific sensation, was sold in 1922 by Banks to the publisher of New York George Plimpton for only $ 10.
This was 322 on account of the plate in the collection of Plimpton, so it was called Plympton 322. After the death of the publisher, the collection was donated to Columbia University.
Scientists have called this tablet one of the most unique mathematical artifacts in the world. After deciphering the cuneiform signs, it turned out that on the clay a sequence of Pythagorean triples was recorded.

What it is? You probably remember from the school course of mathematics the expression "Pythagorean pants in all directions are equal"? So, the Pythagorean triples are an ordered set of three natural numbers (x, y, z), which correspond to the lengths of the sides of a right triangle. In this case they must satisfy the quadratic equation x2 + y2 = z2 from the Pythagorean theorem.
Recall, the theorem says: the sum of the squares of the legs is equal to the square of the length of the hypotenuse.Only 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 common opinion: what purpose did this tablet serve? The matter was further complicated by the fact that the left side of the plate was split off and in the hands of historians was an incomplete text. For a long time it was believed that this was a manual for teachers of mathematics. Allegedly, using this "cheat sheet", the teachers checked whether the children solved the square 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 that is completely unknown to us, which is ahead of its time by 3000 years," says Professor Mansfield. - Plimpton 322 is a powerful computational tool, it was used for architectural calculations in the construction of palaces, temples, step pyramids, channeling and accurate determination of the boundaries of land holdings.

Australian mathematicians claim 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-digit system of calculus. Now this system is used only for measuring time (1 hour consists of 60 minutes, and a minute of 60 seconds) and angles (for example, the circular panorama around you is divided by 360 degrees).
The old Babylonian system is better suited for accurate trigonometric calculations because the modern decimal allows too much error. Conditionally speaking, in the decimal system you can not divide the base number 10 without the remainder 10 by 3 or 4. The exact value you get when dividing 10 is only 5 and 2. But the sixty-digit calculus allows you to divide the base unit without a remainder - 60, to a much larger number fragments.

"I do not recall the times when the ancients could teach the modern world something new," says Daniel Mansfield. - Plimpton-322 is for today the world's only fully accurate trigonometric table, it exceeds modern trigonometry. After 3000 years, Babylonian mathematics can return to fashion. It has a huge potential for application in geodetic work or for solving computer graphics problems.

For a long time the father of trigonometry was called the ancient Greek scholar Hipparchus. He lived in the second century BC and was the first to compose an analogue of modern tables of trigonometric functions. However, it turns out that the Babylonians had a much more accurate mathematical knowledge 1500 years before Hipparchus. It is a pity that we will never know the names of the Sumerian perelmens.
DOSSIER

Plimpton 322 - a sign from the Sumerian city of Lars, which was written about 1800 BC. e. By this time the city was conquered by the Babylonian kingdom and lost its independence. On the front side of the artifact is a table consisting of 15 rows and 4 columns filled with cuneiform signs. Made from clay and has a size of 12.7 cm by 8.8 cm. The left side of the artifact is broken off, but the scientists found that in the original the full text of the trigonometric table contained 6 columns and 38 lines.