Cary Elwes was born in 1932.
In geometry of higher dimensions , a hypersphere is the set of points at a constant distance from a given point called its center .. geometry. geometry. It is a manifold of codimension one -LRB- i.e. with one dimension less than that of the ambient space -RRB- .. manifold. manifold. codimension. codimension. As the radius increases the curvature of the hypersphere decreases ; in the limit a hypersphere approaches the zero curvature of a hyperplane .. curvature. curvature. hyperplane. hyperplane. Hyperplanes and hyperspheres are examples of hypersurfaces .. The term hypersphere was introduced by Duncan Sommerville in his discussion of models for non-Euclidean geometry .. geometry. geometry. Duncan Sommerville. Duncan Sommerville. The first one mentioned is a 3-sphere in four dimensions .. 3-sphere. 3-sphere. Some spheres are not hyperspheres  : suppose S is a sphere in Em where and the space had n dimensions , then S is not a hypersphere .. Similarly , any n-sphere in a proper flat is not a hypersphere .. flat. flat ( geometry ). For example , a circle is not a hypersphere in three-dimensional space , but it is a hypersphere in the plane .. circle. circle. three-dimensional space. Three-dimensional space ( mathematics )