Each side of the yellow square is 2 feet long. In the Meno, Socrates asks a slave boy how long would be the side of a square that had twice the yellow square’s area. The boy guesses first 4 feet, then 3, and finds himself at a loss.

Socrates builds a square four times the size of the yellow one, then divides each of its constituent squares in half with a diagonal. The area of the blue square is thus twice that of the yellow one, and its side has the length we’d sought.

“Some things I have said of which I am not altogether confident,” Socrates tells Meno. “But that we shall be better and braver and less helpless if we think that we ought to enquire, than we should have been if we indulged in the idle fancy that there was no knowing and no use in seeking to know what we do not know; that is a theme upon which I am ready to fight, in word and deed, to the utmost of my power.”