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Spheres in 4-D (Posted on 2003-12-20) Difficulty: 5 of 5
Derive the formula for the 4-D volume of a hypersphere.

See The Solution Submitted by Brian Smith    
Rating: 3.2000 (5 votes)

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re: Answer is Calculus Comment 6 of 6 |
(In reply to Answer is Calculus by CC)

Your first two examples are both for spheres. By analogy, the third, whatever it is, would be for a sphere, not a hypersphere. The proper "series" sequence is from circle to sphere to hypersphere. The area of a circle is pi*r^2. The volume of a sphere is (4/3) pi * r^3. In this progression, one is not the integral of the previous, but rather a composed integral of previous (lower dimension) values as given in the preceding posts.
  Posted by Charlie on 2003-12-28 11:19:08

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