Origami is the art of folding paper into various patterns without cutting or tearing the paper. By viewing the paper as the complex plane, we record all intersection points to construct mathematical origami sets. Additionally, we include the various lines through the intersection points to create a repeating pattern that can be viewed as a wallpaper group. There are 17 wallpaper groups up to isomorphism, so we determine which such groups can be constructed via origami, depending on the rotational and reflectional symmetries that are present in the given pattern. We discuss the relation to various number fields and their corresponding rings of integers, as well as a potential generalization to vector spaces over p-adic fields instead of real vector spaces.
Wallpaper group structure of origami constructions
Sara Chari, St. Mary's College of MarylandAuthors: Sara Chari; Quinn Macauley
2023 AWM Research Symposium
Number Theory at Primarily Undergraduate Institutions [Organized by Bella Tobin and Leah Sturman]