3 ms·
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 a
by endtime 17y ago
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?
- sp332 17y agoLonger explanation, with pictures: http://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem http://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem
- endtime 17y agoThanks, but as far as I can tell that still doesn't actually answer my question.
- rottencupcakes 17y agohttp://www.ics.uci.edu/~eppstein/junkyard/geom-color.html 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.
- endtime 17y agoAh, 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.
- deleted 17y ago[deleted]