Analysis of YBC 7289
Across the diagonal is written 1 24 51 10 = 1 + 24/60 + 51/3600 + 10/216000, which is 1.41421296 to 9 significant decimal figures. The true 9-figure approximation to the square root of 2 is 1.41421356! The 30 at upper left presumably represents a somewhat arbitrary dimension assigned to the side of the square. The length of the diagonal, on this assumption, is 30 times the square root of 2, which is 42 25 35 in base 60. The point really is that the Babylonians knew that the ratio of diagonal to side was exactly the square root of 2, and they knew how to find a good approximation to that number. You can't get such accuracy with measurements by rulers and a pencil. |