Good example. It's amazing how quickly you leave the rationals, even with a square, you almost immediately need numbers that can't be expressed as the ratio of

Good example. It's amazing how quickly you leave the rationals, even with a square, you almost immediately need numbers that can't be expressed as the ratio of two integers... historically, was that the first encounter with an "irrational" number (Pythagorean theorem applied to a right isosceles triangle)? I do remember the proof from number theory about 20 years ago, though I could never recreate it now from memory.