Two properties of stereographic projection on convex bodies in E^3 characterize the sphere: axial symmetry of cones from N and rotation-induced homothety between sections and their projections.
Morales-Amaya, J
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A characterization of the sphere in terms of the stereographic projection
Two properties of stereographic projection on convex bodies in E^3 characterize the sphere: axial symmetry of cones from N and rotation-induced homothety between sections and their projections.