Algebraic number theory and anything else I feel like telling the world about
Monday, May 14, 2007 in calculus, geometry
We compute the “surface areas” of -dimensional spheres. Of course, we know that . Raising this to the power gives . Making the substitution gives . Hence .
Taking the limit as yields a surprising consequence: the surface areas of spheres of radius 1 tend to 0 as the dimension increases!
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Create a free website or blog at WordPress.com.Ben Eastaugh and Chris Sternal-Johnson.
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