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Geometry of möbius transformations : elliptic, parabolic and hyperbolic actions of SL2, (R) /
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 auth...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London, UK : Singapore :
Imperial College Press ; World Scientific,
2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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. |
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| Descripción Física: | 1 online resource (xiv, 192 pages) : illustrations |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9781848168596 1848168594 |