Los Angeles Math Circle

5/11 -- High School II Circle: Impossible Tilings 1

This lecture is about tilings of plane polygons by other plane polygons. We shall see many examples of impossible tilings but the proofs will get more and more involved. Colouring argument is a simple yet strong argument. However, there are problems that colouring argument alone cannot solve. One way of tackling tiling problems is using Conway's tiling group. This method transforms tiling problems into creating specific group structures.