Winner of 2009 JMM Art Award Reveals Science Fundamentals via Origami

April 29, 2009

Goran Konjevod needs only a sheet of paper to challenge—and enlighten—students about basic principles of mathematics, science, and engineering.

Konjevod, an assistant professor of computer science and engineering at Arizona State University, often instructs a class to try to construct models of, say, a bridge via origami. The fundamentals of, for example, load-bearing capacity, structural stress, tension, resistance, and curvature then become easier to grasp.

"I want them to see the mathematical aspects exhibited in the way materials behave, and to think like designers, to think how they would devise models to show what actually happens when you fold the paper in certain ways," Konjevod said.

Konjevod is so good at what he does that last January, at the Joint Mathematics Meetings in Washington, D.C., his combination of origami and mathematical modeling skills led to a first-place prize at the Exhibition of Mathematical Art. His origami work, titled "Wave," bested the creations of three dozen artists in a competition of "aesthetically pleasing works that combine mathematics and art." Representatives of the MAA and the American Mathematical Society judged the entries.

"Wave" is a pleat tessellation whereby a series of parallel folds, or pleats, are formed into a Z-shape, creating a layering effect that triggers a structural tension, which produces a three-dimensional curvature.

Annalisa Crannell, one of the judges and a professor of mathematics at Franklin & Marshall College, said Konjevod's prize-winning piece was good for both the eyes and the brain. "It's all using straight folds, so it should be pretty obvious that you're going to get something straight," Crannell said. "But [Konjevod's piece] is really organic and curvy."

"One of the things I like about both mathematics and art is I can be surprised by something I thought I understood before," Crannell said.

"Wave" is also one origami example of simplicity and complexity coexisting in the world of design, mathematics, engineering, and science. Understanding how to shape materials so as to create specific kinds of folding and layering has led to technological advances such as stents in medicine and compact telescopes for use in space.

Yet the wonders of origami sometimes lead to more mysteries, such as those of protein folding.

"Proteins can fold themselves into shapes that are complicated," Konjevod observed. "What are the physical rules that guide this folding? It's something nature does on it own, yet we don't have an equation to explain how this happens so that we could replicate it."

"I would love to write a computer program that solves the mystery of how to model what paper will do when you fold it in specific ways," said the origami master and award winner.

The art award that Konjevod won was established thanks an anonymous donor who wanted to recognize works "that demonstrate the beauty and elegance of mathematics expressed in visual form." The donor's desire has, for the moment, been fulfilled.

Source: Arizona State University, March 27, 2009; Arizona State University, April 2, 2009.