Derive the formula for the 4-D volume of a hypersphere.
(In reply to Answer is Calculus
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