How did the Babylonians know √2 up to six digits?

The greatest known computational accuracy in the ancient world

This clay tablet from 1800-1600 BC shows that ancient Babylonians were able to approximate the square root of two with 99.9999% precision.

How did they do it?

This tablet from 1800-1600 BC contains √2 with 99.9999% accuracy

Deciphering the tablet

First, let’s decipher the tablet itself. It is called YBC 7289 (short for the 7289th item in the Yale Babylonian Collection), and it depicts a square, its diagonal, and numbers written around them. Here is a stylized version from the book Episodes from the Early History of Mathematics by Aaboe Asger.