The Map Theorem Solved!

THE FOUR COLOR MAP THEOREM

On this link is a book review about the Four Color Map Theorem. This is about why in all the history of map makers no proof it would take more than four colors to color any map has been seen. No one has solved this by a simple proof even with hundreds of years of mapmakers. Here's my own proof;


Two types of regions ("countries") may exist on any map; countries with no holes like usual countries we live in, or countries with more than one hole; math and map authors say the countries with no holes have what's named "Genus 0" and countries with more than one hole have "genus 1" "Genus 2", and so on with the Genus number for the number of holes.


In the middle of any border area is, by definition a country. A country is by definition a unit of one. It's a hole with a country outside, or a country, which is essentially a hole inside out, both have a border that's defined just by a loop. If it has a hole with countries inside this border, each of these countries if with no holes are counted as to be a center country because they are a unit of one. This would always count as one color of the four colors of the Four Color Map Theorem. (The addition of this explanation of the holes is for the sake of completeness, about the mapmakers who would say the proof is incomplete without the more general math so important to that science for other uses.)


For the center countries with Genus 0 (The First Color of The Four Colors of the Theorem) and no holes, or indeed any border (which is always a closed loop) the number of countries on that border must be either odd or even, there are no other counting numbers than odd or even numbers. An odd number is always just an even number + one more.


To achieve both border situations and the other Three Colors, just two are used to make all even numbers of surrounding nations with even numbered borders, and one more if another nation is added. No more are needed if the central nation uses just one color and its border nations would use Two Colors if the border countries were even in number, of either the border or the border inside out, and no more than one more would be used if the surrounding nations were of non even number, total, 4.


That's it! That's my proof Who types out a 1000 volumes, your printer will achieve authors afterlife!

If had just a month left to live it would be in the cute mapmaker marm's arms up at our college, she's powered by GPS..
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