it's true because i said so, QED.

the last problem on my homework set for this week goes:

A closed volume is bounded by conducting surfaces that are the n sides of a regular polyhedron (n = 4, 6, 8, 12, 20). The n surfaces are at different potentials Vi, i = 1, 2, ..., n. Prove in the simplest way you can that the potential at the center of the polyhedron is the average of the potential on the n sides of the boundary surface.

the following is my answer to the problem:



i really really hope the professor does not whack my face with a baseball bat for pulling such a retarded proof. i mean, if i were the one teaching the course and one of my students turned in such a cheap solution like this, i'd want to at least bitchslap that punk.

but whatever. i'm done. time to sleep.