The chromatic number of the plane is at least 5

One of the coolest open problems in math is the chromatic number of the plane (CNP), that is, the Hadwiger–Nelson problem. Considering it has a unit-distance embedding in the plane, the Moser spindle ensures that CNP is at least 4. Furthermore, one may tile the plane with hexagons of the appropriate size and then color those … Continue reading The chromatic number of the plane is at least 5