Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!cornell!batcomputer!riley
From: riley@batcomputer.tn.cornell.edu (Daniel S. Riley)
Newsgroups: comp.sys.amiga.tech
Subject: Re: Re: Clicking on Irregular Shapes (and the four color problem)
Message-ID: <8346@batcomputer.tn.cornell.edu>
Date: 7 Jul 89 15:00:25 GMT
References: <8325@batcomputer.tn.cornell.edu> <36590001@hpindwa.HP.COM>
Reply-To: riley@tcgould.tn.cornell.edu (Daniel S. Riley)
Followup-To: sci.math
Organization: Cornell Theory Center, Cornell University, Ithaca NY
Lines: 27

In article <36590001@hpindwa.HP.COM> chuckh@hpindwa.HP.COM (Chuck Hacala) writes:
>>                  ...  However, it really isn't very useful for the problem
>> at hand.  Most geographical maps are *not* maps in the mathematical sense.
>> For instance, you can't color a map of the US with four colors.
>Why not?  I'm sure I've seen maps of the US with only four colors.  What makes
>a US map not a map in the mathematical sense?

I should have been more careful in that statement.  On further reflection,
I'm not positive that you can't color the US with four colors.  What I
should have said is that the four color theorem doesn't apply to a map of
the US.  One reason is Michigan, which is non-contiguous.  In the case of
Michigan, you can get around the problem by including part of the Great
Lakes in the state.  In general, though, it's fairly easy to construct maps
which obviously require more than four colors if you are allowed to use
non-contiguous regions.  I believe there are other reasons why the four
color theorem doesn't apply to a map of the US, but I should probably go
reference hunting before making any more rash statements.

Since this discussion has wandered off of Amiga's, I'm redirecting
followups to sci.math.

-Dan Riley (riley@tcgould.tn.cornell.edu, cornell!batcomputer!riley)
-Wilson Lab, Cornell U.

p.s.  Gratuitous Amiga content:  VLT V4.036 (the version on the latest Fish
disks) does indeed have some scrolling problems.  I just was bit for the
first time while editting this message.