Definition:Sphere

Definition
The $$n \ $$-dimensional sphere is the set:


 * $$\mathbb S^n = \left\{{x \in \R^{n+1} : \left|{x - y}\right| = r}\right\} \ $$

where $$r \in \R_+ \ $$ is called the radius of the sphere and $$y \in \R^{n+1} \ $$ is called the center of the sphere.

Frequently, the radius is taken as 1 and the center as the origin.