- For spheres in hyperspace, see n-sphere.
In
geometry of higher dimensions, a
hypersphere is the set of points at a constant distance from a given point called its
center. The surface of the hypersphere is a
manifold of one dimension less than the ambient space. As the radius increases the
curvature of the hypersphere decreases; in the limit a hypersphere approaches the zero curvature of a
hyperplane. Both hyperplanes and hyperspheres are
hypersurfaces.