Foolproof

Socrates, drawing figures in the sand, undertakes to coach an untutored slave boy, helping him to prove a special case of the Pythagorean theorem. I paraphrase very loosely:
Socrates: Here is a square with sides of length 2 and area equal to 4. If we double the area, to 8 units, what will the length of a side be?

Boy: Umm, 4?

Socrates: Does 4 x 4 = 8?

Boy: Okay, maybe it's 3.

Socrates: Does 3 x 3 = 8?

Boy: I give up.

Socrates: Observe this line from corner to corner, which the erudite among us call a diagonal. If we erect a new square on the diagonal, note that one-half of the original square makes up one-fourth of the new square, and so the total area of the new square must be double that of the original square. Therefore the length of the diagonal is the length we were seeking, is it not?

Boy: Whatever.

At this point I trust we are all rooting for the kid. I would like to be able to report that the dialogue continues with the boy taking the initiative, saying something like, "Okay, dude, so what's the length of your erudite diagonal? It's not 4 and it's not 3, so what is it, exactly?" Alas, Plato reports no such challenge from the slave boy.

More here.