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Why doesn't this figure disprove the four color theorem?

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Before I ever knew what the "Four color theorem" was, I noticed that I could divide up a map into no more than four colors. I use this all the time when creating texture maps for 3D models and other uses. If 5 colors are needed, then it's wrong, I backup and find the mistake. If you pay attention it always works the first time. read more

The four color theorem does not state that any arbitrary coloring of a map will only contain four colors (obviously not true). It only states the existence of such a coloring. The provided figure is an example of a poor choice of colors. read more

Four Color Theorem', referring to the mathematical problem doesn't necessarily have anything to do with actual maps or countries, as having a mathematical theorem dependent on whatever the current political boundaries would be absurd. read more

It doesn't matter which color is assigned to which region, as all arrangements are interconvertible by symmetry operations on the figure, as partially colored in step (1). Observe that there is exactly one segment of the middle ring that borders both C 2 and C 3 from the inner disk; it also, perforce, borders C 1 from the outer ring. read more

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Why doesn't this figure disprove the four color theorem ...
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