Solved a mathematical puzzle of 3,700 years

The analysis of a Babylonian text written in mud more than 3,700 years ago may have solved one of the oldest enigmas of mathematics. Two Australian researchers have just published the results of their study of Plimpton 322, a cuneiform writing tablet dating back to 1800 BC and coming from the ancient city of Larsa, south of present-day Iraq. The text contains series of numbers arranged in fifteen rows and four columns. They are thought to be Pythagorean triples, series of three numbers that indicate the lengths of the three sides of right triangles.


The one that is probably the most famous mathematical theorem of the world says that the square of the hypotenuse is equal to the sum of the squares of the cathets in a rectangle triangle. The primary students learn that it was formulated by Pythagoras – Greek philosopher and mathematician of the sixth century BC – laying the foundations of trigonometry, the measurement of triangles. What the textbooks do not tell is that 1,000 years before the Babylonians already knew this mathematical proposition and used it in a habitual way, although nobody knows why.  The tablet analyzed is a Rosetta stone of the mathematics of ancient Babylon, the first civilization of history. Nestled between the Tigris and Euphrates rivers, this empire was the epicenter of an unprecedented scientific and cultural revolution that preserves hundreds of thousands of clay tablets used for accounting, mathematics, astronomy and other disciplines.


The mathematician Daniel Mansfield,together with his colleague Norman Wildberger has just proposed that this tablet is the oldest trigonometric table in the world and also the most accurate. Each of its rows is the description of a triangle based on the Pythagorean triples that follow the theorem of the Greek mathematician.



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