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Concept information

geometry > differential geometry > conformal geometry > Möbius transformation
geometry > projective geometry > Möbius transformation
geometry > geometric transformation > Möbius transformation

Terme préférentiel

Möbius transformation  

Définition(s)

  • n geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form

    of 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 the 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 geometries and their transformations generalize this case to any number of dimensions over other fields.
    Möbius transformations are named in honor of August Ferdinand Möbius; they are an example of homographies, linear fractional transformations, bilinear transformations, and spin transformations (in relativity theory).
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/M%C3%B6bius_transformation)

Concept(s) générique(s)

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http://data.loterre.fr/ark:/67375/PSR-J86R5RZW-4

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RDF/XML TURTLE JSON-LD Dernière modif. 08/08/2023