The Babylonians would have mastered the calculation of triangles-rectangles fifteen centuries before the Greeks, according to an Australian study. Is it so safe?
Plimpton 322 clay tablet.
This is a bold hypothesis proposed by Australian researchers and which has been around the world:“Sydney-based scientists have discovered the function of a famous 3,700-year-old Babylonian clay tablet, which turns out to be to be the oldest and most accurate trigonometric table in the world, and which scribes probably used to calculate how to build palaces and temples or dig canals “Explains the press release from the University of New South Wales (Australia). The reality actually appears more nuanced for Christine Proust, historian of mathematics at the University of Paris-VII:"The communication that has been made around this work is exaggerated, these are only hypotheses for the time being “, she tempers.
The Plimpton 322 clay tablet carries 15 rows of numbers that could have been used like a trigonometric table, to calculate how to build temples or palaces.
What is it about ? The tablet in question is known as "Plimpton 322", named after the New York collector George Plimpton who bequeathed it in the 1930s to Columbia University (New York, United States) where it is located. still. The size of a postcard, it has 15 lines of numbers in cuneiform characters, according to a sexagesimal system (in base 60, as for counting our hours). Numbers which, in 1945, could be identified with what mathematicians call "Pythagorean triples". They relate the three sides of a triangle-rectangle, so that the sum of the squares of the length and the width is equal to the square of the diagonal (3, 4 and 5 for example). “The left part of the tablet is missing, and the lines on the reverse indicate that the document is unfinished. The authors obviously had the ambition to list, by the means of calculation at their disposal, all the rectangles whose sides and diagonal were expressible by sexagesimal numbers - 38 in all », Reports, admiringly, Christine Proust.
"It's an attractive hypothesis"
But what could document service be like no other? While some experts see it as abstract mathematics, with no particular purpose, most assume that it was used for school exercises... False! retort Australian mathematicians Daniel Mansfield and Norman Wildberger. According to them, it was used in the manner of a trigonometric table, which since ancient Greece makes it possible to deduce the dimensions of a triangle-rectangle from an angle and a single side. Thanks to the sexagesimal numeration, which has more divisors than the decimal system (base 10), it would also be much more precise than that of Hipparque, calculated the two academics. “That’s an attractive hypothesis, concedes Christine Proust. But it is not supported by any text testifying to the use of a tablet of this type to solve the triangle-rectangle. It is also inappropriate to speak of "trigonometry before the hour », because this one is based on the notion of angle… totally unknown at that time!