Your conjecture as to the surface area of a hypersphere embedded in 4 dimensions (a "3-sphere") is not borne out :) The answer is in fact d^3 pi^2 / 4. See ht

Your conjecture as to the surface area of a hypersphere embedded in 4 dimensions (a "3-sphere") is not borne out :) The answer is in fact d^3 pi^2 / 4. See https://en.wikipedia.org/wiki/N-sphere#Volume_and_surface_area https://en.wikipedia.org/wiki/N-sphere#Volume_and_surface_ar...