I can't believe I haven't blogged about the coolest math fact ever yet. It is not easy to prove—which is another way of saying that I couldn't prove it. I solicited proofs on an internet board, though, and I got one that I could understand. Which I might post in a couple of weeks when I have time over my spring break.
Divide the circumference of a unit circle into n equal arcs with points P_0, P_1, ...P_(n-1). From P_0, draw the n-1 chords that connect it to the other points. Since it's a unit circle and the points are equally spaced, the lengths of these n-1 chords depend only on n. Now find the product of the lengths of the n-1 chords. Try to guess at the punchline, which I'll type between the asterisks below in white type...you can highlight it to see the theorem when you're ready.
*The product of the lengths of the n-1 chords always equals n.*
I know...for you non-math people, that doesn't sound amazing. But...it's soooOOOOooooOOO hard to describe how improbable that result is. I'm sure the mathies in your life will back me up on that.