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Geometry of Mb̲ius transformations elliptic, parabolic and hyperbolic actions of SL2(R)

This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provide.

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  • "Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL₂(R)"@en
  • "Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL₂(R)"

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  • "This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provide."@en
  • "This book is a unique exposition of rich and inspiring geometries associated with Mobius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL[symbol](real number). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F. Klein, who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic Mobius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered."@en

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  • "Electronic books"@en

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  • "Geometry of Möbius transformations elliptic, parabolic and hyperbolic actions of SL2(R)"
  • "Geometry of Möbius transformations : Elliptic, parabolic and hyperbolic actions of Sl_2(R)"
  • "Geometry of Mb̲ius transformations elliptic, parabolic and hyperbolic actions of SL2(R)"@en
  • "Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL₂[real number]"@en
  • "Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL₂[real number]"
  • "Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL₂(R)"@en
  • "Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R)"@en
  • "Geometry of möbius transformations : elliptic, parabolic and hyperbolic actions of SL(2,R)"
  • "Geometry of Möbius transformations elliptic, parabolic and hyperbolic actions of SL₂[real number]"
  • "Geometry of Möbius transformations : elliptic, parabolic and hyperbolic actions of SL2(R)"

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