Illustrating the Pythagorean Theorem and the Square Root of Two

Circa 1900 to 1700 BCE


Yale YBC 7289, one of the few cuneiform tables to consist entirely of a geometrical diagram, shows that Babylonian scribes knew the Pythagorean Theorem and possessed a method of calculating accurate estimates of square roots. 

On the obverse, the scribe drew a square and its diagonals.

"According to Pythagoras' Theorem the length of the diagonal is the length of the side multiplied by the square root of 2. An accurate approximation of this quantity in sexagesimal notation is written along one diagonal. One side is labelled with its length, and the product of this number by the square root of 2 is also written along the diagonal" (, accessed 11-23-2010).

The tablet was acquired by 1944  by the Yale Babylonian Collection.

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