Hypercubes circumscribed in hyperspheres: a constant growth ratio for volumes at large dimensions

الأصل · EN

This note shows that an interesting property arises when considering the relation between the hypersphere volumes at dimensions n+1 and n, if the hyperspheres circumscribe unitary hypercubes in n+1 and n dimensions, respectively. In the limit of large n, the ratio Vₙ₊₁Vₙ is constant and equal to the irrational number √πe/2. Some consequences of this result are explored.