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Hands folding origami

Practical Beauty

 

What does the Japanese art of origami paper folding have in common with science and math? Just think of the precise folding of vehicle airbags and space satellite solar panels.

It’s those connections that intrigue Galen Pickett, CSULB associate professor of physics and astronomy.

 “My main interest is in geometrics—how shapes fit together to make interesting patterns. That’s what my physics research was on before I started with origami,” he said. “It was how polymers arrange themselves into patterns. As a kid, I cut paper up, glued sticks together and made all sorts of geometric models, but I didn’t realize that geometric paper modeling was as developed as it is until I got a random Christmas gift. Three years ago, my wife got me a book on geometric origami.”

Galen PickettHe recalled making simple origami crane birds and other shapes in elementary school, “but I didn’t realize that there is serious geometry going on in origami. For someone that has an innate interest in shapes and someone who has done a lot of research in how shapes organize themselves into structures, origami is a natural thing to work on.”

Those interactions resulted in some 70 research papers being presented at the Fourth International Conference on Origami in Science, Mathematics and Education (4OSME) last September at Caltech in Pasadena. Moreover, the Unitarian Universalist Church of Long Beach recently displayed a number of his artistic creations based on concepts that were the topics of Pickett’s three 4OSME presentations.

“Each one of these things, even though they’re sitting in frames, are machines. They’ve got interesting ways to transmit forces across each other,” he explained, holding up an exquisitely intricate square that curls into a tube that took him four hours to fold. A number of researchers are creating mechanical geometric objects at the micron scale and smaller, a technology field called microelectromechanical systems, or MEMS. For example, silicon wafers of around 10 microns can be fashioned into mirrors, gears or oscillators, he said.

“Origami is about taking flat things and making complex three-dimensional structures with them,” he continued. “The state of the art right now is to have one or two folds that can react to something,” but the hope is to create objects with millions of folds “that will grab hold of a particular thing, twist it and then release it—actual machines that will pick things up and do work.”

 One challenge in turning origami into something practical is to first make the folds, then have the object shrink into the desired shape. “It’s a real puzzle,” Pickett said of his four-hour creation. “How do you make sharp creases like that? It’s like building with Legos while wearing oven mitts. The only thing you can do is to push from both sides, and that’s what I did. You twist the paper; you can press it in different spots until it’s the way that you want it and then you crush it. If everything is lined up right, then it collapses to make the thing I want it to—the target structure. But I want to be able to give a recipe to do that a million times, not just for one piece of paper.

“One of the papers I submitted to 4OSME was on how to get membranes to fold themselves reliably and controllably. This pattern itself is kind of interesting,” he said, referring to the flexible tube he made. “There are some biomedical applications,” including microscopic arterial stents. “What I’ve done at the moment is take a strategy I used to make this by hand which involves applying a slight curvature to the object while you press it. That’s something I discovered just making the thing so that I could have something nice to put on my mantel. I’ve taken that strategy and put it on a computer and found out what you have to do to make this sheet converge into a useful tube as opposed to some random crumple.”

Pickett also is investigating a possible drug delivery system based on other origami concepts developed at Caltech. “If you’ve got this set of Legos and you’re wearing oven mitts and you want to build something, one thing you can do is make sure that different Legos have different attractions for each other so that when you scoop them together, the red one always sticks to the blue one. And if the red one always sticks to the blue one, then you’ll always get a nice column of red, blue, red, blue. Then once that thing is big enough, you can build something else with it. The idea I have using that sort of synthesis is to make ordered polymers with regular shapes self-assemble from those sorts of interactions.”

He found a novel use of DNA to make this occur. “I want to self-assemble loops that are entwined in just the right way, so the morphology I have in mind, oddly enough, is the same linking pattern as medieval Japanese chain mail. The idea is that you have a membrane made of loops, so it’s very flexible and soft but it can hold something, like a bag. The thing holding the stitches of the bag together are these little overlapping fragments of DNA which bind to each other,” forming a network. “If you put in the right DNA fragments,” for example, those that would react to cancer cell DNA, the links would open to release a drug directly near the cancer cells.

Pickett is recognized as both an exceptional scholar and teacher, qualities that earned him a 2006 CSULB outstanding professor award. Origami in education was part of 4OSME, so he wrote about the origami geometry and physics class he volunteered to teach during the summer for the Gifted and Talented Education (GATE) program at his children’s elementary school.

He helped fourth grade students design origami boxes to hold the maximum amount of material as well as create objects holding as much weight as possible. “They found out that one of the structures we made was holding up 2,000 times its weight. I asked them to measure these sorts of things,” in keeping with science education standards.

The class was a learning experience for him, as well. “I really got stumped during week five of the summer. A kid looked up and said, ‘Can you make any animals? Can you make a flower or something?’ And I had to say, ‘No, I can’t make an animal. We can make some more cool shapes. Maybe you can make an animal and teach me how.’”