Abstract: Given a polygon in the plane, you can always triangulate it with straight lines. There is a game you can play with this triangulation: take two triangles that are glued together (they form a quadrilateral), and swap out their shared edge with the opposite diagonal of the quadrilateral. This gives a new triangulation. You can keep doing these “flips” to get new triangulations of the polygon. There is an interesting question: is this game ever boring? That is, are there polygons such that no flip is possible? We explore this question in dimensions two and three, ending with a recent result by me. Lots of pictures and interactive stuff! Lots of fun!
Mathematics Seminars and Colloquia