Arithmetic and Weaving in Antiquity
A pebble proof of the incommensurability in the square
 
 
 

This means that you will not be able to express the ratio between side and diagonal in square by integers. On the other hand, the doubling of a square is so easy that Socrates (in Plato's dialogue "Meno") can even ask an uneducated boy (or slave) to do it. The drawing you see here is a result of the conversation between Socrates and the slave, and this conversation is known in the history of mathematics as the very first geometry-lesson.