This Old Babylonian school tablet shows a problem dealing with the ratio of the length of the diagonal of a square to the length of its side. It demonstrates that the Babylonians knew that the length of the diagonal of a square is equal to the length of its side multiplied by the square root of two (v2), and it shows that they had an excellent approximation of the value of V2.

Three numbers are inscribed:

a = 30, the length of the side of the square
b= 1,24,51,10
c = 42,25,35, the length of diagonal

It can be shown that c = a. b if b and c are written with semicolons in their correct places in order to show place-value notation and thereby differentiate whole numbers from fractions:

b = l;24,51,10 (= 1 + 24/60 + 51/60² + 10/60³)
c = 42;25,35 (= 42 + 25/60 + 35/60²)
That is, 30 . l;24,51,10 = 42;25,35

Using the "Pythagorean Theorem," c² = 2 a&sup...