MIT’s Open Courseware is a wonderful thing. Recently I’ve been watching Erik Demaine’s lectures on the math behind origami.
They’re really fun lectures, and it’s a very interesting subject. I love the sense of humor and play which infuses everything in this area of mathematics. As he introduces one key theorem, he mentions that it was proved during the time of the Bug Wars, and some of the important example cases have names like Frog Base and Waterbomb Base.
The web site for the lectures is really nice. It displays the illustrations and notes in separate windows. As the lecture progresses, these windows keep changing to show you the correct notes.
If you’d like a gentle introduction to this subject, check out Joseph O’Rourke’s book How to Fold It: The Mathematics of Linkages, Origami, and Polyhedra. It’s basically a small paperback version of the course’s textbook, which is known as GFALOP.