Nicolaas Vroom 4 Color theorem

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4 Color theorem

Acryl on canvas 80 by 30 cm

The idea behind this painting is to demonstrate the 4 color theorem with only a difference of one country. The top part shows 37+13 countries and the bottom part shows 38+13 countries.

The 4 color theorem claims that it is possible to color any combination of countries with only 4 colors. Here we use an extra rule, namely the constraint that there is no point where 4 countries meet each other.

The top part and the bottom part are almost each other mirror image of a strange animal. The only difference that the tongue of the bottom image is divided in two. This rather small difference has a hugh influence of the colors of the countries involved. 17 countries keep their own color and 20+1 are changed (not including the 13 countries of the legs and the tail).

There exist also an excel program which allows you to draw a map with any number of countries. This is the reason that 4 countries are not allowed to touch each other at one point. For more detail select: Four Color Theorem

The painting was made before the excel program in roughly 5 hours. Before you start painting, the first thing to do is to draw a sketch with all the countries involved. Next you give each country a number between 1 and 4 to indicate its color. During the painting I realised that not all the countries had the correct number(color). This caused some real troubles. The background color yellow also caused some extra complications.

The excel program can not be used to color the different states of the united states with only 4 colors because the four states Arizona, Utah, Colorado and New Mexico meet each other at one point. (Four corners monument). The program contains an example how to solve this issue.
The same is true for Canada because the 4 states Northwest-Territories, Nunavut, Saskatchewan and Manitoba also meet each other at one point.

With the excel program you can try to beat the 4 color theorem. Have fun.