A visual proof that 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1

7-d Hypercube

Many people are familiar with what a 3-d cube looks like when it's projected onto 2-d space-- it's that box we all draw. This is what a 2-d representation of a 7-dimensional cube looks like.

The construction of Hilbert's space-filling-curve.

This is probably the most important image in Chaos theory- of the Lorenz attractor. It is an illustration of what many people know as the butterfly effect- the concept that a slight change could result in a hugely different outcome.

The image corresponds to the function in three dimensions of two different variables that differ by a very small amount.

This simply constructed shape known as the Hawaiin Earring causes a lot of trouble in the mathematical field of topology, where it is often a counterexample of many intuitive statements.