Origami: Doing the Math Without the Numbers

January 6, 2009

To mathematician Rona Gurkewitz of Western Connecticut State University, in Danbury, origami is "math without numbers."

"I think it is interesting to take an idea and see how far we can go with it," she told Waterbury's Republican-American newspaper. Start with a square. "Will it work on a triangle? An octagon? A decadon?" she asked. "It's playing with shapes and seeing what is going to happen. It teaches me about the relationship between shapes."

One of her shapes, called "The Egg," is made up of 48 linked triangles. Each triangle is the result of 10 folds, and these triangles interlock to form a latticework arrangement that displays square, hexagonal, and pentagonal spaces. Another origami structure, called "Gyroscoped Egg," is an inverse reflection, or dual, of "The Egg." Each vertex of the first structure is turned into a face, and each face is turned into a vertex. Each opening is replaced by a three-dimensional variant of the same shape.

These forms took years to design, Gurkewitz said. The two pieces each have 500 to 600 folds.

Gurkewitz got a taste of this ancient Japanese artform three decades—and thousands of folds—ago. Gurkewitz has since lectured about the teaching potential of origami and written books about the craft. Her most recent book (with Bennett Arnstein), Beginner's Book of Modular Origami Polyhedra: The Platonic Solids (Dover), came out last June.

Gurkewitz is now creating paper quilts, which is a new form of framed, one-dimensional modular origami. "I believe geometry is beautiful," Gurkewitz said. "Now it is beautiful to look at as well as to do"—especially without the numbers!

Source: Republican-American, Waterbury, Conn., Dec. 3, 2008.