Pythagoras’ Theorem in Ancient Mesopotamia

One of the more clear extant proofs of the knowledge of Pythagoras’ theorem by the ancient Mesopotamians is the clay tablet YBC 7289 (Yale Babylonian Collection). We can see in the tablet a square in which the two diagonals are drawn and three numbers are the clues to understand this representation. First of all, next to one of the four sides we can read the number 30 which is the measure of the side. The other two numbers are written in the middle of the square: 42;25,35 and 1;24,51,10 (in sexagesimal notation). The first one is the corresponding measure of the diagonal and it’s equal to the product 30 · 1;24,51,10 so it’s not difficult to deduce that 1;24,51,10 is the value of the corresponding square root of 2. This value is a very accurate approximation of the real value because we can compute:

1,24,51,102 = 1,59,59,59,38,1,40 

If we want to see the details of the tablet we can read page 27 of the book by A.Aaboe entitled Episodes from the Early History of Mathematics, Washington, D.C.: MAA, 1998 (originally published in 1964) which is possible to find very easy in internet:

Location: University of Yale (Yale Babylonian Collection)

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