Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Riemann_sphere> ?p ?o }
- Riemann_sphere abstract "In mathematics, the Riemann sphere, named after the 19th century mathematician Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value ∞ for infinity. With the Riemann model, the point "∞" is near to very large numbers, just as the point "0" is near to very small numbers.The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as 1/0 = ∞ well-behaved. For example, any rational function on the complex plane can be extended to a continuous function on the Riemann sphere, with the poles of the rational function mapping to infinity. More generally, any meromorphic function can be thought of as a continuous function whose codomain is the Riemann sphere.In geometry, the Riemann sphere is the prototypical example of a Riemann surface, and is one of the simplest complex manifolds. In projective geometry, the sphere can be thought of as the complex projective line P1(C), the projective space of all complex lines in C2. As with any compact Riemann surface, the sphere may also be viewed as a projective algebraic curve, making it a fundamental example in algebraic geometry. It also finds utility in other disciplines that depend on analysis and geometry, such as quantum mechanics and other branches of physics.".
- Riemann_sphere thumbnail Stereographic_projection_in_3D.png?width=300.
- Riemann_sphere wikiPageExternalLink moebius.
- Riemann_sphere wikiPageID "30876799".
- Riemann_sphere wikiPageLength "19513".
- Riemann_sphere wikiPageOutDegree "110".
- Riemann_sphere wikiPageRevisionID "680036119".
- Riemann_sphere wikiPageWikiLink Addition.
- Riemann_sphere wikiPageWikiLink Algebraic_curve.
- Riemann_sphere wikiPageWikiLink Algebraic_geometry.
- Riemann_sphere wikiPageWikiLink Atlas_(topology).
- Riemann_sphere wikiPageWikiLink Automorphism.
- Riemann_sphere wikiPageWikiLink Bernhard_Riemann.
- Riemann_sphere wikiPageWikiLink Biholomorphism.
- Riemann_sphere wikiPageWikiLink Cartesian_coordinate_system.
- Riemann_sphere wikiPageWikiLink Cartesian_coordinates.
- Riemann_sphere wikiPageWikiLink Category:Projective_geometry.
- Riemann_sphere wikiPageWikiLink Category:Riemann_surfaces.
- Riemann_sphere wikiPageWikiLink Category:Spheres.
- Riemann_sphere wikiPageWikiLink Celestial_sphere.
- Riemann_sphere wikiPageWikiLink Chart.
- Riemann_sphere wikiPageWikiLink Closed_manifold.
- Riemann_sphere wikiPageWikiLink Codomain.
- Riemann_sphere wikiPageWikiLink Compact_space.
- Riemann_sphere wikiPageWikiLink Compactification_(mathematics).
- Riemann_sphere wikiPageWikiLink Complex_analysis.
- Riemann_sphere wikiPageWikiLink Complex_line.
- Riemann_sphere wikiPageWikiLink Complex_manifold.
- Riemann_sphere wikiPageWikiLink Complex_number.
- Riemann_sphere wikiPageWikiLink Complex_plane.
- Riemann_sphere wikiPageWikiLink Complex_projective_plane.
- Riemann_sphere wikiPageWikiLink Conformal_equivalence.
- Riemann_sphere wikiPageWikiLink Conformal_geometry.
- Riemann_sphere wikiPageWikiLink Conformal_manifold.
- Riemann_sphere wikiPageWikiLink Constant_curvature.
- Riemann_sphere wikiPageWikiLink Continuous_function.
- Riemann_sphere wikiPageWikiLink Cross-ratio.
- Riemann_sphere wikiPageWikiLink Dessin_denfant.
- Riemann_sphere wikiPageWikiLink Determinant.
- Riemann_sphere wikiPageWikiLink Diffeomorphism.
- Riemann_sphere wikiPageWikiLink Differentiable_manifold.
- Riemann_sphere wikiPageWikiLink Directed_infinity.
- Riemann_sphere wikiPageWikiLink Division_(mathematics).
- Riemann_sphere wikiPageWikiLink Division_by_zero.
- Riemann_sphere wikiPageWikiLink Douglas_N._Arnold.
- Riemann_sphere wikiPageWikiLink Equivalence_relation.
- Riemann_sphere wikiPageWikiLink Field_(mathematics).
- Riemann_sphere wikiPageWikiLink Fubini–Study_metric.
- Riemann_sphere wikiPageWikiLink Gaussian_curvature.
- Riemann_sphere wikiPageWikiLink Gauss–Bonnet_theorem.
- Riemann_sphere wikiPageWikiLink General_relativity.
- Riemann_sphere wikiPageWikiLink Geometry.
- Riemann_sphere wikiPageWikiLink Group_(mathematics).
- Riemann_sphere wikiPageWikiLink Holomorphic_function.
- Riemann_sphere wikiPageWikiLink Hopf_bundle.
- Riemann_sphere wikiPageWikiLink Hopf_fibration.
- Riemann_sphere wikiPageWikiLink Hyperbolic_space.
- Riemann_sphere wikiPageWikiLink Infinity.
- Riemann_sphere wikiPageWikiLink Isometry_(Riemannian_geometry).
- Riemann_sphere wikiPageWikiLink Limit_of_a_function.
- Riemann_sphere wikiPageWikiLink Linear_map.
- Riemann_sphere wikiPageWikiLink Linear_transformation.
- Riemann_sphere wikiPageWikiLink Manifold.
- Riemann_sphere wikiPageWikiLink Manifold_with_boundary.
- Riemann_sphere wikiPageWikiLink Mass.
- Riemann_sphere wikiPageWikiLink Mathematical_model.
- Riemann_sphere wikiPageWikiLink Mathematics.
- Riemann_sphere wikiPageWikiLink Meromorphic_function.
- Riemann_sphere wikiPageWikiLink Metric_tensor.
- Riemann_sphere wikiPageWikiLink Multiplication.
- Riemann_sphere wikiPageWikiLink Multiplicative_inverse.
- Riemann_sphere wikiPageWikiLink Möbius_plane.
- Riemann_sphere wikiPageWikiLink Möbius_transformation.
- Riemann_sphere wikiPageWikiLink O(3).
- Riemann_sphere wikiPageWikiLink Orientation_(mathematics).
- Riemann_sphere wikiPageWikiLink Orientation_(vector_space).
- Riemann_sphere wikiPageWikiLink Oriented_surface.
- Riemann_sphere wikiPageWikiLink Orthogonal_group.
- Riemann_sphere wikiPageWikiLink Photon.
- Riemann_sphere wikiPageWikiLink Photon_polarization.
- Riemann_sphere wikiPageWikiLink Physics.
- Riemann_sphere wikiPageWikiLink Point_at_infinity.
- Riemann_sphere wikiPageWikiLink Pole_(complex_analysis).
- Riemann_sphere wikiPageWikiLink Projective_geometry.
- Riemann_sphere wikiPageWikiLink Projective_line.
- Riemann_sphere wikiPageWikiLink Projective_space.
- Riemann_sphere wikiPageWikiLink Quantum_bit.
- Riemann_sphere wikiPageWikiLink Quantum_mechanics.
- Riemann_sphere wikiPageWikiLink Qubit.
- Riemann_sphere wikiPageWikiLink Quotient_space_(topology).
- Riemann_sphere wikiPageWikiLink Quotient_topology.
- Riemann_sphere wikiPageWikiLink Rational_function.
- Riemann_sphere wikiPageWikiLink Riemann_surface.
- Riemann_sphere wikiPageWikiLink Riemannian_manifold.
- Riemann_sphere wikiPageWikiLink Riemannian_metric.
- Riemann_sphere wikiPageWikiLink Rotation.
- Riemann_sphere wikiPageWikiLink Rotation_group_SO(3).
- Riemann_sphere wikiPageWikiLink SO(3).
- Riemann_sphere wikiPageWikiLink Scaling_(geometry).
- Riemann_sphere wikiPageWikiLink Simply-connected.