You've got to love an essay that has the following paraphrase of Plato's Meno dialog:
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.
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.
