In the making of origami, one starts with a piece of paper, and through a series of folds along seed points
one constructs complicated three-dimensional shapes. Mathematically, one can think of the complex
numbers as representing the piece of paper, and the seed points and folds as a way to generate a subset of
the complex numbers. Under certain constraints, this construction can give rise to interesting mathematical
structures. We will talk about the basic construction of an origami ring and further extensions and
implications of these ideas in algebra and number theory.