Re: Four color theorem: why this is not a proof and pointer to simple explanations

Hello, Andre:

I think it's neat that your son thought so much about it. Keep encouraging
him.

I think the error in his reasoning is that if five colors are necessary,then
it must be due to five countries touching.

What if an island was divided this way: draw two concentric circles, and
slice the region between them into seven parts by drawing segments from one
circle to the other. Now color this. You never have four countries
touching each other, yet you will need four colors in the map of this
island.

What made the Four-Color Problem hard was the effort needed to insure that
there were not things like this happening that would force the use of a
fifth color.

--charlie

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