Origami and Math

Chloe Cheng, RHS ‘07

Origami is not just a recreational activity of young Japanese children. It requires mental acrobatics and deep focus. Nevertheless, the mathematics behind the art may be the most fascinating and complicated aspect of origami. If you unfold a work of origami, you will see a complex geometric pattern, even if the model you folded was a simple one. In order to produce many origami models, you must be able to divide the side of a square sheet of paper into equal pieces. Induction can prove how such a task can be accomplished with any number of equal pieces. Aside from induction, other mathematical relationships, including Huzita’s axioms and Kawasaki’s theorem, can be linked to origami. Huzita’s axioms are a set of rules related to the mathematical principles of paper folding, and Kawasaki’s theorem concerns the angles produced by the creases in the model. Origami construction can also be used to solve the famous “problems of antiquity,” such as doubling a cube or trisecting an angle.