Find Surface Area of an N-Dimensional Sphere

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In summary, the speaker mistakenly posted a question about finding the surface area of an n-dimensional sphere in the wrong section and received insufficient answers. They had encountered this concept in a stat-mech class but never fully understood it and were now seeking help with a derivation and explanation. They were also curious about the concept and had not been able to give it the attention it deserved due to other academic responsibilities. They clarified their question and expressed their gratitude for the responses they had received in the math forum.
  • #1
fizixx
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Hello everyone...

I mistakenly posted this question in a math section, met with insufficient answers. :frown: My fault there, but here's the gist:

How do you find the surface area of an n-dimensional sphere?​

I ran across this concept in a stat-mech class a long, long time ago...didn't understand it very well at the time. It was an aside kind of thing the prof did during a lecture. I thought if I spent a little one-on-one time with the concept I would 'get it', but the rigors of homework, research, etc disallowed the quality time intended, so I ended up putting this into my mental closet for rainy-day thinking, and of course, never got back to it, but I'm still very curious about it.

Can someone do this derivation and explain the thinking behind it please?


:confused:
 
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  • #2
fizixx said:
How do you find the surface area of an n-dimensional sphere?

what do you mean "find"? do you want an epression for the amount of surface "area" of an n-dimensional sphere, given a "radius"?
 
  • #3
Looks to me like you have plenty of responses in the math fourm.
 

FAQ: Find Surface Area of an N-Dimensional Sphere

What is the formula for finding the surface area of an N-dimensional sphere?

The formula for finding the surface area of an N-dimensional sphere is S = 2π^(N/2) * r^(N-1), where S is the surface area and r is the radius of the sphere.

Can the surface area of an N-dimensional sphere be calculated using the same formula as a 3-dimensional sphere?

Yes, the formula for finding the surface area of a 3-dimensional sphere is a special case of the general formula for an N-dimensional sphere. However, the radius in the general formula may be different depending on the number of dimensions.

How does the surface area of an N-dimensional sphere change as the number of dimensions increases?

The surface area of an N-dimensional sphere increases as the number of dimensions increases. This is because as the number of dimensions increases, the volume of the sphere also increases, resulting in a larger surface area.

Is there a limit to the number of dimensions for which the surface area of a sphere can be calculated?

No, the formula for finding the surface area of an N-dimensional sphere can be applied to any number of dimensions. However, as the number of dimensions increases, the calculations become more complex.

Can the surface area of an N-dimensional sphere be negative?

No, the surface area of any sphere, regardless of the number of dimensions, cannot be negative. It is a physical property that represents the total area of the sphere's surface, and it cannot have a negative value.

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