球の表面積や体積計算で楽しんでいるKidsが私塾の老先生の下で超球について学んでいる。私は習ったことすらなし!2次元、3次元ならなんとかわかるが4,5,6次元になるとどうなるの?
2項定理の展開式のようなものか。(a + b)^6 = a^6 + .............+b^6
Hyperspheres
zeta137.blogspot.jp
As reported in wikipedia: en.wikipedia.org/wiki/Hypersphere, a hypersphere is the set of points at a constant distance from a given point called its center.
The "volume" of a hypersphere is given by:
where Γ denotes the gamma function.
The "surface area" is instead given by: