Solve the mystery finds the real Indiana Jones

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Babylonian clay tablet, created 3700 years ago, contains a more accurate trigonometric table than those which are now used modern mathematics.

This artifact belonged to the American diplomat and collector of antiquities Edgar banks. Today this man is more famous as the prototype of Indiana Jones, the hero of a series of adventure movies, which brilliantly plays the iconic Hollywood actor Harrison Ford.

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Plimpton 322 — a tablet from the Sumerian city of Larsa, which was written around 1800 BC.

In 1898, banks assumed the post of American Consul in Baghdad, and apart from the service, were engaged in that hundreds bought the ancient cuneiform clay tablets from the «black diggers» and resold them to museums. Earthenware plate, which became a real scientific sensation, in 1922, was sold to banks publisher new York George Plimpton for only $ 10.

This was 322 account sign in collection Plimton, so it is called Plimpton 322. After the death of the publisher of the collection was donated to Columbia University.

Scientists have named this sign one of the most unique mathematical artifacts in the world. After deciphering the cuneiform characters was found that the clay contains the sequence of Pythagorean triples.

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What is it? You probably remember from the school course of mathematics the expression «Pythagorean pants on all sides are equal»? So, Pythagorean triples is an ordered set of three positive integers (x,y,z) that correspond to the lengths of the sides of a right triangle. However, they must meet the square equation x2 + y2 = z2 Pythagoras ‘ theorem.

Recall that the theorem States: the sum of the squares of the legs equals the square of the hypotenuse long. Just a small trifle — this plate was written by the Sumerians at least 1000 years before Pythagoras’s birth.

For a long time scientists could not come to the same conclusion: for what purpose was served this plate? This was compounded by the fact that the left side of the plate has been cleaved, and in the hands of historians were incomplete text. For a long time it was thought that it was a Handbook for teachers of mathematics. Supposedly, using this «cheat sheet» the teacher checked whether the children solved quadratic equation.

However, mathematics Daniel Mansfield, and Norman Wildberger from the University of New South Wales (Australia) claim that no relation to the child’s play this artifact has not.

— Actually it is a trigonometric table based on the completely unknown method to us, which is ahead of its time in 3000 years, according to Professor Mansfield. The Plimpton 322 is a powerful computational tool used for architectural calculations in the construction of palaces, temples, stepped pyramids, strip channels and a precise definition of borders of land holdings.

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Australian mathematicians say that a trigonometric table ancient Babylonians allows you to make more accurate calculations. The fact that they were not decimal, but sexagesimal system of calculation. Now this system is only used for measuring time (1 hour consists of 60 minutes and a minute of 60 seconds) and corners (e.g., circular view around you is divided into 360 degrees).

The old Babylonian system is better suited for accurate trigonometric calculations since the modern decimal allows for too much error. Relatively speaking, in the decimal system you will not be able without a remainder divide the base 10 number 3 or 4. The exact value you get when dividing 10 only 5 and 2. A sexagesimal calculation allows no residue to divide the base unit 60, the number of fragments.

— I do not remember cases, when the ancient could teach the modern world is something new, — says Daniel Mansfield. Plympton — 322 is today the world’s only completely accurate trigonometric table, it is superior to modern trigonometry. After 3000 years of Babylonian mathematics may come back into fashion. It has enormous potential for use in surveying or for the decision of tasks of computer graphics.

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For a long time the father of trigonometry called the ancient Greek scientist Hipparchus. He lived in the second century BC and the first made similar to a table of trigonometric functions. However, it appears that the Babylonians over 1500 years prior to Hipparcos had a much more precise mathematical knowledge. It is a pity that the names of the Sumerian Perelman we’ll never know.


Plimpton 322 — a tablet from the Sumerian city of Larsa, which was written around 1800 BC By this time the city was conquered by the Babylonian Kingdom and lost its independence. On the front side of the artifact shows a table with 15 rows and 4 columns, filled with cuneiform signs. Made of clay and has a size of 12.7 cm by 8.8 cm on the Left side of the artifact is broken, but the researchers found that in the original full text of the trigonometric tables contain 6 columns and 38 rows.

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