On the mathematics of origami

From TED: "Robert Lang is a pioneer of the newest kind of origami -- using math and engineering principles to fold mind-blowingly intricate designs that are beautiful and, sometimes, very useful."

A very cool talk on the geometry of coral reefs.

From TED: "Margaret Wertheim leads a project to re-create the creatures of the coral reefs using a crochet technique invented by a mathematician -- celebrating the amazements of the reef, and deep-diving into the hyperbolic geometry underlying coral creation."

About fractals...

From TED: "'I am a mathematician, and I would like to stand on your roof.' That is how Ron Eglash greeted many African families he met while researching the fractal patterns he’d noticed in villages across the continent."

Arthur Benjamin, a mathematician, does some amazing mental math:

Toward the end of the video, he explains his process. What principle is he using? You should all recognize it.