# Origami – The Math Behind the Paper Folding

I am about to start teaching an online geometry course, and it has me missing some of the things I use to do with my students to help them discover relationships, and work with angles and symmetry, which was origami. Origami is the art of paper-folding – and using it in geometry is a great hands-on and visual tool to help students discover angle relationships, symmetry, linear relationships.

Origami is something I am sure most of you are familiar with and maybe have even attempted to create some origami art yourself. I have two friends who are origami wizards and often post their creations on FB – and it’s pretty amazing the shapes they create. When I recently went to the Museum of Math in NYC there was a whole exhibit devoted to Origami.

In my class, obviously, we did relatively simple constructs – folding one piece of paper into things like cubes, birds, shapes. The focus being on the folding and shapes created from each fold and looking at the angles and relationships that developed after each fold. But – as I have discovered, there is some really complex math behind origami, and really complex shapes that are created all from one sheet of paper that are simply astounding. I just found this Ted Talk from 2008 by Robert Langdon that discusses the mathematics behind Origami and how because of mathematics, folds that before were impossible are now possible, allowing for origami constructions that are astounding. Those of you who teach geometry, I think this will be very interesting to you, though I think other math subjects as well will find some applications. At the end of the video there is also a link to some templates for folding some more intricate origami constructs.