June 5th, 2018, 09:06 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 444 Thanks: 29 Math Focus: Number theory  Pack unit circles on unit sphere
What is the maximum number of nonoverlapping unit circles that can be packed upon a unit sphere?

June 5th, 2018, 09:26 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,530 Thanks: 1390 
You're going to have to expand on what you mean by "packed upon". If you mean that every point on the circle intersects the surface of the sphere... wouldn't every such circle have the center of the sphere as it's center? I.e. they will all overlap. 
June 6th, 2018, 11:08 AM  #3  
Senior Member Joined: May 2015 From: Arlington, VA Posts: 444 Thanks: 29 Math Focus: Number theory  Quote:
Since a sphere is a surface, this situation (the maximum number of unit, nonintersecting circles upon a unit sphere) is akin to other packing problems (circles within a circle, spheres within a cube, etc). By "packed upon," here I mean filling (in three dimensional space) a twodimensional boundary (a unit sphere) with twodimensional shapes (unit circles) that do not overlap (i.e., are mutually exclusive). Do I use the word "upon" incorrectly? Maybe "resting upon" is better.  
June 6th, 2018, 12:17 PM  #4  
Senior Member Joined: Aug 2012 Posts: 2,356 Thanks: 738  Quote:
 
June 6th, 2018, 08:02 PM  #5  
Senior Member Joined: May 2015 From: Arlington, VA Posts: 444 Thanks: 29 Math Focus: Number theory  Quote:
 

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circles, pack, packed, sphere, unit 
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