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Vol. LXIV, No. 25
December 7, 2012
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Demaine Finds the Math Behind Pleats and Folds, Mountains and Valleys

On the front page...

Dr. Erik Demaine

Dr. Erik Demaine

Although the Japanese art of origami originated centuries ago, only in recent decades have the underlying mathematics governing folding come to light. One of its most light-hearted yet deep-thinking adherents visited NIH on Nov. 2 to explain that mathematical algorithms lie behind not only the paper folds that yield a swan, but also the elegant folding techniques that allow space-based telescopes to unfurl and car airbags to deploy safely.

Dr. Erik Demaine may be the poster boy for home-schooled Canadian artist-scholar prodigies. In an enthusiastic introduction to his talk, Dr. Michael Gottesman, NIH deputy director for intramural research, noted that Demaine entered Dalhousie University at age 12, got his bachelor’s degree at 14 then earned his Ph.D. at the University of Waterloo, “Canada’s MIT.”

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Demaine joined MIT’s faculty at age 20, Gottesman continued, making him what is thought to be the school’s youngest professor ever. At age 23, Demaine received a MacArthur Foundation “genius” grant. While NIH frequently hosts math whizzes, widely cited scientists and even artists, they rarely come in a single package, Gottesman noted.

“He is a generous and gregarious collaborator…and an artist too,” he added. Demaine’s art, which grows directly out of his science, is currently on display at the Renwick Gallery in Washington, D.C., and is also represented at the Museum of Modern Art in New York City, among other institutions.

Demaine was able to illustrate some of his concepts by gestures and body language. Demaine was able to illustrate some of his concepts by gestures and body language. Demaine was able to illustrate some of his concepts by gestures and body language.

Demaine was able to illustrate some of his concepts by gestures and body language.

Photos: Bill Branson

Demaine himself is a lanky, genial, pony-tailed tour guide through a world that, though highly abstract, is clearly full of play and imagination. It’s just that the play involves words such as bidimensionality, hinged dissections and hyparhedra. Making his first visit to NIH, Demaine, now 31, gave two talks on Nov. 2, a morning session for scientists and a general-audience talk in the afternoon.

The “easy” session began with an explanation of folding algorithms that underlie a wide variety of commonly observed phenomena. “Linkage folding” is what your arm and elbow can do, or what robotic arms are capable of aboard space stations. The algorithms get harder as one progresses from 1 dimension through dimensions 2, 3, 4 and 5.

Examples of 2-dimensional folding include stents, unfolding telescopes and airbags, which can start out essentially flat in their compacted versions, then bloom into useful shapes. Three-dimensional folding includes solids, Transformer-type toys and sheet-metal fabrication.

“Mathematics is really fun, beautiful and hard,” Demaine said, “and so is the art.”

Demaine gave two talks on Nov. 2, a morning session for scientists and
a general-audience talk in the afternoon

Making his first visit to NIH, Demaine gave two talks on Nov. 2, a morning session for scientists and a general-audience talk in the afternoon. His art, which grows directly out of his science, is currently on display at the Renwick Gallery in Washington, D.C., and is also represented at the Museum of Modern Art in New York City, among other institutions.

His presentation relied heavily on slides, videos and Demaine himself cutting up flat pieces of paper along one straight line to yield examples of origami. But there are biological ramifications of his work as well. He is anxious to know why proteins fold so easily; the pure geometry of how it occurs fascinates him.

“I believe that nature is a computer,” he declared.

The largely youthful crowd that came to hear Demaine’s afternoon talk was treated to illustrations of two algorithms for origami design, both available as free software. He showed how “TreeMaker” designs a folding of a square into a stick figure that can morph into a lizard or scorpion, and how “Origamizer” designs a folding of a square of paper into a complex 3-D rabbit. Demaine and his team have proven, mathematically, that any 3-D structure can be created from a flat sheet.

Wondering whether robotic paper, which essentially shapes itself, is possible, Demaine and his collaborators created an example, which he demonstrated on video.

The transitions from idea to prototype flow freely in Demaine’s world, and he acknowledged that science and art constantly feed one another.

“You get art using mathematics as a tool,” he said. Sculpture has been the result of his inquiries into folding concentric circles, in which there are pleats and folds, mountains and valleys. “We build [sculpture] to find out what is possible.

“For the past 13 years, we’ve gone from art to science to art, back to science,” he said. “We get more productive art by doing science and we get better science by doing art.”

To learn more about this mutually beneficial feedback loop, visit www.erikdemaine.org or watch his NIH afternoon talk at http://videocast. nih.gov/summary.asp?Live=12051.


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