Polyominoes

With Matt Lee and Nick Woods

two-dimensional figures created by joining squares along their edges - have permeated popular culture through popular games such at Tetris and Blokus. They and their three-dimensional relatives, the polycubes, have interesting mathematical properties and have become objects of study in combinatorics and number theory. Our goal is to explore the relationship between matrix theory and geometry by determining the solvability of certain tiling problems involving polyominoes. Students will then use newly-acquired tools to pose and solve their own questions about these shapes. This project is accessible to all undergraduate students who have taken Math 31; underclassmen are especially encouraged to apply.