Fancy Folding

By Ivars Peterson

Muse, March 2001, p. 24.

The amazing thing about origami is the enormous number of different objects you can make by folding a square sheet of paper. No glue or scissors allowed! You can make airplanes, flowers, butterflies, and noisemakers, or flapping birds, fierce devils, and fully equipped lobsters.

Robert Lang's incredible origami lobster.

Tom Hull, a mathematician at Merrimack College in North Andover, Massachusetts, has been making origami models since he was eight years old. He got started when his uncle gave him a book about origami. When he got to college, Hull found a way to combine his interest in origami with a career in mathematics. He even contributed to a book for beginners, called Origami, Plain and Simple, while he was a student.

Hull is now inventing new types of origami designs based on mathematics. Some of these designs are flat. They look like tiles--the sorts of repeating patterns that you might see in fancy bathrooms, for example. Others are made from identical simple units, each one folded from a square sheet of paper, that interlock to form three-dimensional structures that look like sticky burrs or crazy crystals.

Tom Hull's amazing five intersecting tetrahedron.

Physicist Robert J. Lang likes to work out rules that, when given to a computer, show what creases to make to end up with a desired origami figure. He is famous for highly complex designs, such as his paper lobster, which comes fully equipped with legs, pincers, feelers, and tail.

There's a lot of math in origami, from the patterns the creases make to the sets of precise instructions people follow to create certain objects. Hull himself uses origami to help explain angles and other geometric concepts to students. He also finds origami relaxing after a hard day in the classroom.

Tom Hull has a web page about origami mathematics at http://web.merrimack.edu/~thull/OrigamiMath.html.

The Exploratorium in San Francisco features an illustrated article about origami designs on its Web page at http://www.exploratorium.edu/exploring/paper/index.html .

Mathematician Helena Verrill illustrates a variety of her origami tiling designs and provides instructions for making them at http://hverrill.net/pages~helena/origami/index.html.

You'll find diagrams and instructions for making all sorts of origami figures and patterns at http://www.paperfolding.com/diagrams/.

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