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October 23rd, 2013, 04:00 PM  #1 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0  the total number of points in ndimensional sphere
Hello, Could somebody tell me how to count the total number of points in ndimensional sphere depending on r? I think about it more than week and I can't do this... I know that for 1dimensional sphere it is r*2 + 1. But I can't count it for 2,3.. 10  it's max dimension. Can somebody help me? 
October 23rd, 2013, 05:43 PM  #2 
Senior Member Joined: Dec 2012 Posts: 372 Thanks: 2  Re: the total number of points in ndimensional sphere
Mr. Business Man, nobody can count the number of points in the nsphere for any . What do you possibly want to do with this number?

October 23rd, 2013, 06:07 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,682 Thanks: 658  Re: the total number of points in ndimensional sphere Quote:
 
October 23rd, 2013, 11:16 PM  #4 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0  Re: the total number of points in ndimensional sphere
Sorry, I've forgotten about that. Yes, all coordinates must be integer.

October 24th, 2013, 06:34 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,269 Thanks: 1958 
Try a google search for "The Sphere Problem", but results are rather limited.

October 24th, 2013, 02:18 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,682 Thanks: 658  Re: the total number of points in ndimensional sphere
When you say n is the number of dimensions, your answer for n=1 is a little confusing. A 1 dimensional sphere is a straight line interval, so the number of points covered would be ~ r, not rē. Also is the center of the sphere at the origin? 
October 24th, 2013, 06:43 PM  #7 
Newbie Joined: Oct 2013 Posts: 3 Thanks: 0  Re: the total number of points in ndimensional sphere
The center of the sphere is point 0 in n=1, (0,0) in n=2, (0,0,0) in n=3 and so on. Sorry, I didn't mean I mean: because for r=1 I am going one point to the right, one point to the left and the zero, so the result is 3. for r=2 I am going two points to the right, two points to the left ant the zero, so the result is 5. But I can't imagine how it looks in more dimensional sphere... I searched on google but without any success. 
October 24th, 2013, 07:19 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,269 Thanks: 1958 
Try giving Google additional search terms, such as "integer coordinates".


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