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October 23rd, 2013, 03:00 PM   #1
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the total number of points in n-dimensional sphere

Hello,

Could somebody tell me how to count the total number of points in n-dimensional sphere depending on r?
I think about it more than week and I can't do this...

I know that for 1-dimensional sphere it is r*2 + 1.

But I can't count it for 2,3.. 10 - it's max dimension.

Can somebody help me?
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October 23rd, 2013, 04:43 PM   #2
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Re: the total number of points in n-dimensional sphere

Mr. Business Man, nobody can count the number of points in the n-sphere for any . What do you possibly want to do with this number?
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October 23rd, 2013, 05:07 PM   #3
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Re: the total number of points in n-dimensional sphere

Quote:
Originally Posted by Business Man
Hello,

Could somebody tell me how to count the total number of points in n-dimensional sphere depending on r?
I think about it more than week and I can't do this...

I know that for 1-dimensional sphere it is r*2 + 1.

But I can't count it for 2,3.. 10 - it's max dimension.

Can somebody help me?
There are an infinite number of points, unless you put on some restrictions, such as all coordinates are integer.
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October 23rd, 2013, 10:16 PM   #4
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Re: the total number of points in n-dimensional sphere

Sorry, I've forgotten about that. Yes, all coordinates must be integer.
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October 24th, 2013, 05:34 AM   #5
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Try a google search for "The Sphere Problem", but results are rather limited.
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October 24th, 2013, 01:18 PM   #6
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Re: the total number of points in n-dimensional 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?
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October 24th, 2013, 05:43 PM   #7
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Re: the total number of points in n-dimensional 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.
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October 24th, 2013, 06:19 PM   #8
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Try giving Google additional search terms, such as "integer coordinates".
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