Geometry Of Mobius Transformations: Elli

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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 SL2(R). Starting from elementa…
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    Om Geometry Of Mobius Transformations: Elli

    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 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 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.

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    Detaljer

    Format
    E-Bok
    Kopisperre
    Teknisk DRM
    Filformat
    PDF
    Utgivelsesår
    2012
    Forlag
    World Scientific Publishing Co
    Språk
    Engelsk
    ISBN
    9781848168596
    Sider
    208
    Emne

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