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   Author  Topic: Nine Points on a Sphere  (Read 4065 times)
James Fingas
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Nine Points on a Sphere  
« on: Oct 2nd, 2002, 6:46am »
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Show how to distribute nine points around the surface of a sphere in such a way that each point is equidistant from its four nearest neighbors.
 
// modified post to include problem statement at top - willywutang 5/21/2008


 
The solution to this is quite beautiful. It's like the "trees for Willywutang" question, where you just sort of stumble onto the solution. Here's a hint:
 
The ratio of point-distance to sphere radius is 4*sqrt(6) : 7 + sqrt(2) ...  Grin
 
I'd also like to say that I have found distributions for the following numbers of points on a sphere (each equidistant from 4 neighbours):
 
6, 8, 10, 12, ...
9, 15, 21, ...
 
There seems to be no possible solution for 5 or 7 points, and I'm working on 11...
 
There are also a few distributions for 5 neighbours, but it's a MUCH harder problem in general.
« Last Edit: May 21st, 2008, 3:09pm by william wu » IP Logged

Doc, I'm addicted to advice! What should I do?
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