The Mathematics of Paper Folding
Summer 2009 REU
Led by Prof. Robert Rumely
Origami, the art of paper folding, has deep geometric roots. However, the mathematical theory behind origami has really only been developed within the past twenty years. This REU will focus on learning, applying, and extending that theory.
There are several different styles of origami.
Classical origami focuses on creating models of animals, people, and inanimate objects, with a balance between realism and abstraction depending the taste of the designer. Here, the mathematical theory provides tools for a creating suitable base, or preliminary fold, which can then be folded into the desired object.
Modular origami focuses on creating models of geometric objects, such as the platonic solids, out of simple units which can be linked together. Here the fact that the model is built of many pieces opens the possibility of using different colors, exposing the underlying geometry in fascinating ways.
Tesselation focuses on folding paper into surfaces with repeating patterns, some of which show hidden features when held up to light. Here, geometry and symmetries again play a leading role.
This REU will provide an introduction to paper folding and the mathematics behind it, exploring all of the styles above. Participants will then use the theory to design new models, and investigate open questions in the theory. This REU will run for 7 weeks, from June 8 through July 24.
Prior experience with paper folding is desirable, but not necessary. Participants need to have creativity, good geometric insight, and good fine motor skills; people who enjoy making things typically have those skills. Applicants should document these qualifications, and should have had at least two upper division math courses which involve reading and writing proofs. Applications will be accepted through April 1, 2009.
Student Project Reports
Alex James
Anne Ho
Audrey Hubbard
Brittany Baker
Tory McCoy
Other Reports
Origami REU Report
Origami Box Problem
