Four colors

19 11 2008

Belize, 32mm x 48mm

I like this map stamp because of the way it illustrates the Four Color Map Theorem, which asserts that any map on a plane (or a sphere) can be split up into areas each colored one of just four colors with no two colors adjacent. Here the districts of the country of Belize (formerly known as British Honduras) and the adjacent countries of Mexico and Guatemala are colored yellow, dark brown, green, and reddish brown with no two of the same color touching. A few moments with paper and pencil should satisfy the curious viewer that it is not possible to render this map with only three distinct colors. Maps on more complex geometric objects such as the surface of a torus or a Möbius strip are not able to satisfy this condition with so few colors. Note that the Caribbean does not touch the district of Cayo shown here in dark brown, so by this construction both could have done in blue as well satisfying the constraints of the theorem.

Off the coast of Belize are islands which take on an unusual shape in this issue, the southernmost island looking like a check mark and the more northerly islands near the Mexican state of Quintana Roo in the Yucatan appearing to be more scattered than they are in reality. These are called the Cayes and sit amongst coral reefs much prized by scuba divers visiting the coast. One mainland province of Belize is disconnected from the rest, making up the southern end of a peninsula (shown in reddish brown here) with the town of San Pedro at its tip.