One of my hobbies for a while when I was a young ‘un was origami. It was swiftly overtaken by other arts and crafts, and these were hobbies long before I started taking apart cameras and radios, and the like, to see how they worked, and collecting pondwater and pressing leaves and….
In retrospect, I think it might be obvious that (obstacles aside) I had a good chance of becoming a theoretical physicist. A lot of those arts and crafts hobbies were all about intricate patterns of one sort or another. I loved that stuff, although I did not think of it as mathematics… just a nice pattern. And I was drawn to playing with and creating those patterns. Some of them are amazing, as you know from staring at whatever your mum or grandmother is working on right now. Or perhaps you. I’ll tell you about more of that some other time. Let’s get back 
to origami. I stumbled upon (via NPR) an excellent website, that of Robert J. Lang. It is quite wonderful. The site tells you about Lang’s work, and shows you a ton of it. But the best thing of all is that it tells you about the Art, Science and Mathematics of it all together. The engineering applications of origami are growing as well. These include developing the best way of folding airbags for ready deployment, and the problem of how to fold up a giant array of solar panels on a spacecraft so that they can be successfully unfolded and put into use once the craft gets into space.
Imagine also the problem in a scientific context of how to design arrays of mirrors with complex arrangements which fold the path of light… origami helps in the design. How about the problem of putting an incredibly huge telescope into space, with a ptimary mirror 50 times bigger than Hubble’s? You’d have to fold it somehow. Origami is being used to tackle the problem…
Well, I’ll let you go and look at the site for more information, or just at look at the wonderful pictures of some origami designs. The image of the origami crane above (click for larger) – and the crease pattern underlying it – is from the site. Also, if you’re in the area, you can go to a conference this weekend at Caltech. It is “The Fourth International Conference on Origami in Science, Mathematics, and Education”, and the web information is here. The great and good of the Origami-as-art, and Origami-meets-science world is there, and there are some plenary and parallel sessions there that may be of interest. Looks like they take walk-ins.
-cvj
Artisticly origami is art, but behind it, involves a lot of complex
folding techniques
Say Lee’s comment almost sounds like how a native sculpture says that they see the animal in a piece of stone (wood, ivory, etc) then they remove all the unneeded pieces… See it then unfold it! I love it!
IN regards to Coxeter and Penrose, do you see any value in relating “the sheet” in 2D to tessellations on a sphere, as the origami product of the crane?
Wow! That’s amazing….Thanks……. -cvj
Chanced upon this online article in the Discover Magazine:
http://www.discover.com/issues/jul-06/features/origami/
wherein even Lang is awed by this Japanese Phenom, Satoshi Kamiya, whose modus operandi is sheer human brain power.
To quote the article by Jennifer Kahn:
“Origami aficionados agree that Kamiya’s most extraordinary sculpture is a dragon he created in 2004, at age 20. Coiled and rearing, the dragon has the lithe energy of a living snake, with overlapping scales, thornlike teeth, and tiny, grasping, clawed hands. Asked how he manages to create something so complicated without the help of a computer, Kamiya pauses to consider. “I see it finished,” he says finally. “And then”—he stares off, as though visualizing the imaginary object—”I unfold it. In my mind. One piece at a time.”
and
“Kamiya, too, continues to experiment, but he has no interest in learning to use TreeMaker. In halting English he says: “Right now, human way is better.”