02:58
Some of you probably already know this, but "Gibbs phenomenon" refers to the fact that fourier series approximations will always "overshoot" jumps (like those in a square wave) by a certain amount, no matter how many terms are used in the approximation.
From wikipedia, the overshoot converges (as you add more terms) to 8.9% above/below the jump.
I'm just mentioning this to complain about it. If it's possible for math to be "ugly", IMO this is it.