This class was inspired by the folding method in Build Your Own Polyhedra by Peter Hilton and Jean Pedersen. Using a sequence of up and down folds of a strip of paper, they present a way to fold an (approximately) perfect strip of triangles and other shapes. Using these folded strips as units, you can fold regular polygons, polyhedra, flexagons and more.
The mathematics behind this folding technique starts with iteration and convergence, and goes far. In their follow-up book that I’ve just started reading, A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics, Hilton and Pedersen tie together topics in Number Theory, Group Theory, Platonic Solids and more with beautiful presentation.
Here is the convergence problem set. It triggered a rich mathematical discussion concerning implicit assumptions and explicit formulations, and had many satisfying tangents.Convergence Problems.