Map Coloring on a Torus
Map Coloring on a Torus
Heawood proved that seven colors are sufficient to color a map on the surface of a torus so that no two bordering areas share the same color.
A torus can be constructed by stretching a square until the two pairs of opposite edges can be glued together. Each map used in this Demonstration is a square pattern whose top and bottom match and whose left and right edges match.