# Science Of Origami Mathematicians And Artists Use Algorithms To Make Complicated Paper Sculptures

September 1, 2008 — Mathematicians design new figures in a traditional art form called origami, using modern techniques. Innovations developed in pursuit of the art find application in multiple fields, including applied mathematics and engineering. One application is the use of folding algorithms to pack air bags.

Can a piece of paper save your life? You probably don't know one modern invention was derived from the science of origami, the ancient art of paper folding.

"What first got me as a kid was the idea that you can create all these different shapes from such a simple starting material -- an uncut sheet of paper," says origami artist and engineer Robert Lang, Ph.D.

Origami is the traditional technique of Japanese paper folding. Modern science agrees there's a lot they couldn't do with out this ancient art form.

"Science, technology, space, automotive, medicine -- all these different fields have benefited from origami," Dr. Lang says.

Dr. Lang is one of America's greatest origami artists. He can fold just about anything from a single sheet of paper. He's honored that his art can also be effective for education and invention.

"There has been some testing that shows that after students have done origami, that they have a higher appreciation or understanding of various mathematical geometric concepts," he says.

It's an ancient science that uses mathematics for modern day miracles. The twists and bends in an origami turtle may just make their way into your cell phone's circuit board. And how can a paper scorpion actually save your life? The origami algorithms used to fold bugs are the same ones behind the invention of the air bags in your car.

"An algorithm that origami artists had come up with for the design of insects was the right algorithm to give the creases for flattening an airbag," Dr. Lang said. "So that has now been adopted into airbag simulation code, and presumably automotive engineers are now using those codes to design airbags."

Cal Tech says the applications are endless. From consumer programs to the space program, the options have yet to unfold.

Remember the fortune squares you flipped as a kid? That was a form of origami. So if you told fortunes through torn and tattered paper, you were actually studying science.

ABOUT ORIGAMI: Paper folded into delicate shapes may look like art, but at its foundation is a strong supporting layer of math. Beyond a basic paper airplane or simple animal shape, geometry and mathematical calculations enable the creation of astonishing shapes and designs. People have developed a way of diagramming their creations called sequenced crease patterns, which indicate where to make folds, and in what order.

ORIGAMI REVEALS ANSWERS: Algorithms developed for use in origami have been applied to several other fields. Engineers use the algorithms to design the best way to fold an airbag for optimum deployment and astronomers use them to compute the optimum configuration of space telescope lenses. People use the techniques of origami to design games, puzzles, and even magic tricks.

The American Mathematical Society and the Mathematical Association of America contributed to the information contained in the TV portion of this report.

Note: This story and accompanying video were originally produced for the American Institute of Physics series Discoveries and Breakthroughs in Science by Ivanhoe Broadcast News and are protected by copyright law. All rights reserved.

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