Coloring the Plane by David Goetze '24

Abstract:

Consider every point in the plane. Connect two points if they are distance one from each other. Now, color every point such that is a different color than the points you have connected it to. How many colors would you need? Is it infinitely many or perhaps 7? In this talk, we introduce the Hadwiger-Nelson problem and its many analogs. We will begin with a brief introduction to the world of graphs. Using our new knowledge, we will prove various analogs of the problem before culminating our investigation by proving the best bounds on this decades-old problem.