Since the late 1970s, the art of origami (paper folding) has been
going through a renaissance, both in terms of technical complexity and
artistic expression. Origami artists are now able to fold, from a single,
uncut square, things which no one ever would have thought possible, and
through this are able to achieve levels of realism and expression never
seen before.
Mathematics is largely to blame. A small group of mathematicians,
physicists, and engineers have been discovering the theorems that govern
how paper is folded. Much of this work has led to a deeper understanding
of the paper folding process, which has granted artists greater paper
folding prowess. This talk will survey the theorems behind flat origami
(i.e., origami models that can be pressed in a book without crumpling) and
describe (1) how they can be used in complex origami design, (2) how
technology has assisted and met pitfalls in this field, and (3) how this,
in turn, has found some interesting applications elsewhere in the sciences.
The amount of material I will be able to present will depend entirely
on how much time I have. But to summarize, I plan on presenting theorems
and work of Maekawa, Kawasaki, Meguro, Lang, and myself (skipping most
proofs), and give a rough outline of how this work is used in origami
designs. This leads directly to Lang's TreeMaker algorithm, which allows
basic complex origami design on a computer. This, in turn, branches into
two interesting aspects: (1) how parts of Lang's algorithm turn out to
have applications in the design of easily-collapsible airbags as well as
collapsible materials for use in outer space, and (2) the apparent
contradiction that while researchers have been able to model paper
crumpling on computers, they have not been completely successful in
modeling origami. (There are NP-completeness issues lurking here.) Of
course, I will also have numerous pictures and models of super-complex
origami which will easily drive home the fact that mathematics has led to
increased artistry in the origami field of sculpture.
In short, origami is a great example of the interconnectedness
between mathematics and art. It also showcases the use of technology in
artistic design, although many of the computational problems in modeling
origami on a computer remain unsolved. Furthermore, surprising applications
of origami design exist in engineering, adding yet another interdisciplinary
aspect (in addition to the more obvious cultural ties to Japan) to origami
math. Lastly, most mathematicians (and artists) are completely unaware of
the interesting and beautiful work being done, both mathematically and
artistically, in origami. Thus, including this talk in your session should
attract a healthy crowd.
A 20 minute talk would suffice to summarize all the main points
quickly. Longer would be even better, of course. A computer projector and
overhead projector would both be needed.
For some examples of the level and style of origami I'm referring to here,
see the photos of Satoshi Kamiya's work on my web page:
http://web.merrimack.edu/~thull/kamiya/kamiya.html
Brief info about the author:
I have been practicing origami since I was 8 years old, have authored
two origami instruction books, and for the past 12 years have been
collecting information about and researching origami mathematics. Last
year I organized a conference, the 3rd International Meeting of Origami
Mathematics, Science, and Education, and the proceedings of this conference
have just been published by A.K. Peters.