origami and maths

People who spend time folding paper often ask themselves questions that are ultimately mathematical in nature. Is there a simpler procedure for folding a certain figure? Where on the original square paper do the wings of a crane come from? Why do so many origami figures start with square paper? What size paper should I use to make a chair to sit at the origami table I already made? What words should I use to teach people to make a jumping frog? Is it possible to make an origami beetle that has six legs and two antennae from a single square sheet of paper? Is there a precise procedure for folding a paper into 5 rectangular strips? Which polyhedra can be constructed using Sonobe modules and what do they have in common?

The Challenge Problems section gives some more mathematical origami questions that you might like to think about.

In the last few decades, folders inspired by questions like these have revolutionized origami by bringing mathematical techniques to their art. In the early 1990s, Robert Lang proved that for any number of appendages, there is an origami base that can produce the desired effect from a single square sheet of paper. Robert has created a computer program that can design a somewhat optimized base for any stick figure outline. This has enabled many folders to create origami animals that were considered impossible years ago. You can see some of Robert's creations in these photos on Krystyna Burczyk's web page.