On Wednesday, March 5, 2014 4:35:12 PM UTC-6, swtch...@gmail.com wrote: > Pie chart example makes a good case for not counting a point.
The pie chart example does more than "make a good case". It establishes beyond any coherent and reasonable discussion that one must exclude a point because otherwise the problem has a trivial negative answer.
> In a real world situation.
In the real world, countries are often disconnected, and so there exist maps that require more than 4 colors; and this does not even count the problem of coloring the "sea". But the 4 color map theorem is not about "a real world situation" in full generality, it is about a special kind of map.
> How many two countries share only a point between the two?
In the US, there are two pairs of states that only share a single point: Utah and New Mexico; Colorado and Arizona.
So? It's irrelevant to the fact that the theorem considers only maps in which a single common point does not count as an adjacency.
> So many borderlines to count between diagonally situated countries. > > In the simplified world, diagonally situated countries only share a point > > with each other, never a border. > > Thus the necessity to change the convention of not counting a point.
THEN THIS IS NOT THE 4 COLOR MAP THEOREM and you can stop talking about the theorem, you are talking about something *else*.
> Coloring a map of the square world
Oh, you want to talk about "the real world" but you want countries and the world to be square?
> using a unit function following its rule > > for expanding the coloring scheme for more countries around it guarantees > > that the theorem works.
Since you are not considering the theorem, you are considering something else, anything you say is completely irrelevant to the theorem. Saying "the theorem works" is stupid, because you aren't talking about the theorem, you are talking about something else.
Moreover, the theorem is not about "expanding coloring schemes" or extending partial colorings, it is about the existence of a FULL coloring. So again, you are talking about something else entirely and NOTHING you say has any bearing or relevance to the Four Color Map Theorem. You can stop saying "the theorem works" and "the theorem does not work", because:
YOU AREN'T TALKING ABOUT THE THEOREM. YOU ARE TALKING ABOUT SOMETHING ELSE.
> If the map has a country bigger than the rest on the map, bigger by a multiple of even number and there is at least one more column next to that country to its rightside, the guarantee no longer stands.
> That is all.
More nonsense, completely irrelevant to the 4-color map theorem.