My wife gave me an origami book for Christmas: Origami Design Secrets: Mathematical Methods for an Ancient Art by Robert Lang. It has many folding instructions for some very cool designs. What really stands out about this book is what its subtitle suggests: “Mathematical Methods for an Ancient Art.” That’s right, Lang has gone to the effort to explain why certain folds are used and the mathematical theory behind them. This can result in some very complex designs. Some really amazing things he explains are how to make scales that cover a fish’s body, and how to make long, thin appendages (like for a tarantula.) Every design uses a single piece of paper (sometimes large, sometimes non-square) without any cuts or adhesives.
I’ve started some of the more simples designs, like an emu, snail, and hummingbird. I like the hummingbird a lot. I also did the bull moose design, which was difficult because the many folds required got way too small relative to the size of paper I was using. The largest paper I currently have is 10″ x 10″, and to make the folding easier and to finish with a good looking moose, I think you would need paper nearly twice this size.
After making these designs I now understand and have made most of the basic folds. I plan on next reading the book to learn what Lang has to offer on the theory end of it all. It sounds like after studying this book, a person would have a better idea of how to create their own origami designs.