News: AAAS 2009 Annual Meeting News
The Math of Paper Folding: How Origami can Save your Life
It turns out origami is more useful than making swan napkins at your favorite Chinese restaurant--it might just save your life. But more on that later.
A panel of mathematicians speaking at the 2009 AAAS Annual Meeting in Chicago experts explained how the traditional art of paper folder can be used in the classroom to get students excited about math as well as by engineers to develop the next generation of innovative products.
Thomas Hull, an associate professor of mathematics at Western New England College in Springfield, Massachusetts, said that origami is a great way to teach college students about math because it's hands-on. In addition to geometry, origami incorporates other mathematical disciplines including number theory, networks, matrices, and graph theory.
In teaching geometry, for example, Hull demonstrates to his students that every other angle around all vertices--folds--will always add up to 180 degrees, no matter how complex the fold, so long as it folds into a flat object.
"Paper is your mathematical laboratory," said Hull.
Hull joked that while he knows hundreds of applications for origami outside the classroom, he admits that he once thought that paper-folding had no use for the military. He was wrong.
Hull outlined a program by the U.S. Army to develop microscopic cubic silicon ID tags that could be placed on the uniforms of soldiers and relay in important information about soldier movements and health. The chips would be cubic, allowing unmanned drone planes to fly overhead and read the information by aiming lasers at the three-dimensional object.
Because the chip is microscopic, it is much easier to fold the chip into the cube than to cut and paste the sides together, he said.
Tamara Veenstra, professor of mathematics at the University of Redlands in California, said that many origami designs begin with instructions to divide a piece of paper into prime-numbered parts. This can be a challenge, she said, because traditional origami does not allow the use of a ruler or any device other than the paper itself. But by using the Fujimoto technique of origami--which uses aspects of number theory--one can fold a piece of paper into equal, prime-numbered sections.
Robert Lang, who has his own origami company and designs commission pieces, said that origami has experienced an explosion of new ideas. Using a computer program he developed that takes a stick figure and turns it into a folding pattern, Lang had folded turtles, tarantulas, moose, deer, frogs, praying mantises, and praying mantises eating praying mantises.
In addition to folding paper, Lang said that origami experts have served as consultants by the automobile industry to design airbags; by NASA to fold space lenses, solar sails, and satellites; as well as by medical technology companies in their question to get "bigger things into smaller holes" during surgery.
Lang said that stents, which are inserted into clogged arteries to reduce constriction, and airbags are based on traditional origami designs.
"The stent is based on a origami design called the 'blow up box'," said Lang. "Some of the applications of origami could save your life."
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