Find Surface Area of an N-Dimensional Sphere

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To find the surface area of an n-dimensional sphere, one needs to derive a formula based on the radius of the sphere. The discussion highlights a lack of clarity in previous responses, with a request for a detailed derivation and explanation. The concept is rooted in higher-dimensional geometry, often encountered in advanced mathematics and physics. Understanding the surface area involves recognizing the relationship between dimensions and the geometric properties of spheres. A clear expression for the surface area can enhance comprehension of n-dimensional spaces.
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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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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"?
 
Looks to me like you have plenty of responses in the math fourm.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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