Subject: Re: [BoundaryPoint] Re: Four Color Maps
Date: Dec 07, 2003 @ 06:34
Author: Lowell G. McManus ("Lowell G. McManus" <mcmanus71496@...>)
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----- Original Message -----From: John SeeligerSent: Saturday, December 06, 2003 11:01 PMSubject: Re: [BoundaryPoint] Re: Four Color Maps----- Original Message -----From: "acroorca2002" <orc@...>Sent: Saturday, December 06, 2003 1:32 PMSubject: [BoundaryPoint] Re: Four Color Maps> well i know this has been a perennially interesting question eric
> but how about first showing us a theoretical example of a topology
> requiring a 5th color
> & then at least we will know what to seek on your behalf in reality
>
> otherwise i think we may only continue to peck away at this huge
> offering
> & finally shrug our shoulders
> even if we had the geographical knowledge to apply to itHere is my stab at it. Hopefully, one day the below picture will hang in the Louvre. Start with A, B and C. Color them each a seperate color. Now, surround by D. It must be a fourth color. Now make E, F and G which must be red, yellow and blue, though not necessarily in that order. Now suppose E claims a (purple) swath of land cutting two of the boundaries AC and CB. Come to think of it, it is actually unnecessary for F and G to exist. EFG could be one big red ring on the outside. Then to make that swath, it would have to be a new color, so EFG must now be that color. So the new map would show A, B, C and D, as is and change my EFG outside to just one E and make it purple.