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- Möbius_transformation abstract "In geometry and complex analysis, a Möbius transformation of the plane is a rational function of the formof one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.Geometrically, a Möbius transformation can be obtained by first performing stereographic projection from the plane to the unit two-sphere, rotating and moving the sphere to a new location and orientation in space, and then performing stereographic projection (from the new position of the sphere) to the plane.These transformations preserve angles, map every straight line to a line or circle, and map every circle to a line or circle.The Möbius transformations are projective transformations of the complex projective line. They form a group called the Möbius group which is the projective linear group PGL(2,C). Together with its subgroups, it has numerous applications in mathematics and physics.Möbius transformations are named in honor of August Ferdinand Möbius; they are also variously named homographies, homographic transformations, linear fractional transformations, bilinear transformations, or fractional linear transformations.".
- Möbius_transformation wikiPageID "314493".
- Möbius_transformation wikiPageRevisionID "602526059".
- Möbius_transformation id "p/q076430".
- Möbius_transformation title "Linear Fractional Transformation".
- Möbius_transformation title "Quasi-conformal mapping".
- Möbius_transformation urlname "LinearFractionalTransformation".
- Möbius_transformation subject Category:Conformal_geometry.
- Möbius_transformation subject Category:Continued_fractions.
- Möbius_transformation subject Category:Functions_and_mappings.
- Möbius_transformation subject Category:Kleinian_groups.
- Möbius_transformation subject Category:Lie_groups.
- Möbius_transformation subject Category:Projective_geometry.
- Möbius_transformation subject Category:Riemann_surfaces.
- Möbius_transformation comment "In geometry and complex analysis, a Möbius transformation of the plane is a rational function of the formof one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.Geometrically, a Möbius transformation can be obtained by first performing stereographic projection from the plane to the unit two-sphere, rotating and moving the sphere to a new location and orientation in space, and then performing stereographic projection (from the new position of the sphere) to the plane.These transformations preserve angles, map every straight line to a line or circle, and map every circle to a line or circle.The Möbius transformations are projective transformations of the complex projective line. ".
- Möbius_transformation label "Funkcja homograficzna".
- Möbius_transformation label "Möbius transformation".
- Möbius_transformation label "Möbius-transformatie".
- Möbius_transformation label "Möbiustransformation".
- Möbius_transformation label "Transformación de Möbius".
- Möbius_transformation label "Transformation de Möbius".
- Möbius_transformation label "Transformação de Möbius".
- Möbius_transformation label "Trasformazione di Möbius".
- Möbius_transformation label "Преобразование Мёбиуса".
- Möbius_transformation label "تحويل موبيوس".
- Möbius_transformation label "メビウス変換".
- Möbius_transformation label "莫比乌斯变换".
- Möbius_transformation sameAs M%C3%B6bius_transformation.
- Möbius_transformation sameAs Möbiustransformation.
- Möbius_transformation sameAs Transformación_de_Möbius.
- Möbius_transformation sameAs Transformation_de_Möbius.
- Möbius_transformation sameAs Trasformazione_di_Möbius.
- Möbius_transformation sameAs メビウス変換.
- Möbius_transformation sameAs 뫼비우스_변환.
- Möbius_transformation sameAs Möbius-transformatie.
- Möbius_transformation sameAs Funkcja_homograficzna.
- Möbius_transformation sameAs Transformação_de_Möbius.
- Möbius_transformation sameAs Q595742.
- Möbius_transformation sameAs Q595742.
- Möbius_transformation wasDerivedFrom Möbius_transformation?oldid=602526059.