The intersections between origami, mathematics, and science occur at many levels and include many fields of the latter. We can group these intersections into roughly three categories:

• Origami mathematics, which includes the mathematics that describes the underlying laws of origami;
• Computational origami, which comprises algorithms and theory devoted to the solution of origami problems by mathematical means;
• Origami technology, which is the application of origami (and folding in general) to the solution of problems arising in engineering, industrial design, and technology in general.

These divisions are a bit arbitrary, of course; one genre blends into another. Origami math defines the "ground rules" for computational origami's goal of solving origami design problems (and quantifying their difficulty). The results of computational origami, in turn, can be (and have been) pressed into service to solve technological problems ranging from consumer products to the space program.

In the sections listed to the left, you'll find examples of all three of these intersecting genres. Feel free to explore; there's no particular order.

4OSME

During the last 20 years, there have been 3 highly successful international scientific conferences exploring the interactions between origami, mathematics, and science. Continuing this series, Origami USA, the American national origami society, recently held The Fourth International Conference on Origami in Science, Mathematics, and Education (4OSME), on September 8-10, 2006, at the California Institute of Technology, Pasadena, California, USA. It was a rousing success. Click on the link to the left to learn more information about this exciting event.