OK, well, how about equal spheres in 3-space, non-overlapping except for tangencies, where no two tangent spheres can be the same color. Is there a maximum chromatic numbers for such arrangements, and if so, what is it? --Dan On 2013-04-29, at 6:06 PM, Bill Gosper wrote:
Dave Makin>I assume these "countries" didn't include any "holey" ones i.e. rings etc. ? Connectedness is obviously required. I don't see simple-connectedness mattering.
DM> Also given the equivalent assumptions is the answer for 3D just 5 colours ? Infinity, obviously. Scott Kim once showed me that the answer for *convex* 3D countries is "arbitrarily large".
On 29 Apr 2013, at 13:48, Henry Baker wrote:
FYI -- How is it possible that I never knew that (computer scientist) Andrew Appel was Kenneth Appel's son? Obviously, Appel's don't fall far from the tree... http://www.nytimes.com/2013/04/29/technology/kenneth-i-appel-mathematician-w...
Kenneth I. Appel, Mathematician Who Harnessed Computer Power, Dies at 80
By DENNIS OVERBYE
Published: April 28, 2013
Kenneth I. Appel, who helped usher the venerable mathematical proof into the computer age, solving a longstanding problem concerning colors on a map with the help of an I.B.M. computer making billions of decisions, died on April 19 in Dover, N.H. He was 80.
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DM>The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
And spirituality instigates jihad. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun