A is the area of the base, and I think they integrate it along the height. I'm not sure why they divide by the dimension. I could not find a derivation of that formula.
I found a formula for regular hyperpyramids: Vn = rn/n
An n-pyramid, or n dimensional hyperpyramid, is analogous to a triangle in arbitrary dimensions. It's formed by starting with an (n-1)-cube, and sweeping the cube perpendicular to itself, just as we did in forming an n cube (see hypercubes for a discussion of n-cubes and their volumes).
Question:
(1) Why the sentence in the beginning start with An?
(2) What is sweeping?
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