alexander horned sphere analytic geometry angle antipodal point apollonius of perga arc length archimedes australia ball channel surface circle compact space curvature david hilbert diameter differential equation dimension directional statistics dupin cyclide dyson sphere earth ellipse embedding equator euler angles focal surface fused quartz gamma function gaussian curvature geodesic geoid globose nucleus gravity probe b great-circle distance great circle greek language gyroscope helicoid hoberman sphere homeomorphism homology sphere homotopy groups of spheres homotopy sphere kilogram latitude longitude mathematics mean curvature metric space minimal surface n-sphere natural number parallel postulate physics plane geometry principal curvature pseudosphere radius real number real projective plane refraction riemann sphere riemannian circle rotation group soap bubble solid angle solid geometry specific surface area sphere packing spherical earth spherical cap spherical geometry spherical trigonometry spheroid stephan cohn-vossen surface surface area surface normal surface of revolution surface tension topological manifold topology torus trigonometry umbilical point unit sphere up to volume zoll surface