Visual Proofs



Sometimes, a visual proof is more helpful than pages of computations. Here are two interesting math concepts which you might find interesting.

1. "Dual" of polyhedra -- basically take a solid like a cube, find the midpoint of each edge, and rotate each edge about the midpoint until it connects with the other sides. Those two shapes are "dual". http://hyrodium.tumblr.com/post/76098308148/dual-polyhedrons

2. The "Sum of squares" 1 + 2 + 4 + 9 + 16 + ... has an elegant representation. Just think about stacking blocks and count up how many blocks are in the solid rectangle when you're done:
Proof 1 - fantastic animation! (source) Here is a Non animated 2d proof.