A story of the rise and fall of a serious attempt at a proof that P!=NP

Re:A story of the rise and fall of a serious attempt at a pr... by endtime on Thursday August 20, 2009 @01:42PM (#775608)

A bit tangential, but...

>What is the fewest number of colors sufficient for coloring the plane so that no two points with the same color are a unit distance apart?

For a given point P, aren't there an infinite number of points that are a given distance from P? I.e. the points that correspond to a unit circle with origin at P are all that unit distance from P. What am I missing here?

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Re:A story of the rise and fall of a serious attempt at a pr... by sp332 on Thursday August 20, 2009 @01:56PM (#775651)

Longer explanation, with pictures: http://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem

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Re:A story of the rise and fall of a serious attempt at a pr... by endtime on Thursday August 20, 2009 @02:05PM (#775671)

Thanks, but as far as I can tell that still doesn't actually answer my question.

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Re:A story of the rise and fall of a serious attempt at a pr... by rottencupcakes on Thursday August 20, 2009 @02:17PM (#775713)

http://www.ics.uci.edu/~eppstein/junkyard/geom-color.html

Yes, there are an infinite number of points at a distance 1 from the original point. However, that doesn't matter for the problem.

All you want to do is color regions of the plane such that, for any given point, every point a unit away is in a different colored region.

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Re:A story of the rise and fall of a serious attempt at a pr... by endtime on Thursday August 20, 2009 @06:25PM (#776486)

Ah, right. Not sure why your wording clicked for me (or, rather, I'm not sure why I was being dense before), but makes sense now. Thanks.

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