Geometry of mobius transformations: elliptic, parabolic and hyperbolic actions of SL[symbol]([real number])
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...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
London
Imperial College Press
c2012
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| Subjects: | |
| Online Access: | FHN01 Volltext |
| Summary: | 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 |
| Physical Description: | xiv, 192 p. ill |
| ISBN: | 9781848168596 |
Staff View
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| author | Kisil, Vladimir V. |
| author_facet | Kisil, Vladimir V. |
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| author_sort | Kisil, Vladimir V. |
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| dewey-full | 516.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.1 |
| dewey-search | 516.1 |
| dewey-sort | 3516.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044633528 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:42Z |
| institution | BVB |
| isbn | 9781848168596 |
| language | English |
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| physical | xiv, 192 p. ill |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Imperial College Press |
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| spelling | Kisil, Vladimir V. Verfasser aut Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) Vladimir V. Kisil London Imperial College Press c2012 xiv, 192 p. ill txt rdacontent c rdamedia cr rdacarrier 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 Mobius transformations Möbius-Geometrie (DE-588)4750877-2 gnd rswk-swf Kleinsche Gruppe (DE-588)4164159-0 gnd rswk-swf Transformation (DE-588)4451062-7 gnd rswk-swf Möbius-Geometrie (DE-588)4750877-2 s Kleinsche Gruppe (DE-588)4164159-0 s Transformation (DE-588)4451062-7 s DE-604 Erscheint auch als Druck-Ausgabe 1848168586 Erscheint auch als Druck-Ausgabe 9781848168589 http://www.worldscientific.com/worldscibooks/10.1142/P835#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Kisil, Vladimir V. Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) Mobius transformations Möbius-Geometrie (DE-588)4750877-2 gnd Kleinsche Gruppe (DE-588)4164159-0 gnd Transformation (DE-588)4451062-7 gnd |
| subject_GND | (DE-588)4750877-2 (DE-588)4164159-0 (DE-588)4451062-7 |
| title | Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) |
| title_auth | Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) |
| title_exact_search | Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) |
| title_full | Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) Vladimir V. Kisil |
| title_fullStr | Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) Vladimir V. Kisil |
| title_full_unstemmed | Geometry of mobius transformations elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) Vladimir V. Kisil |
| title_short | Geometry of mobius transformations |
| title_sort | geometry of mobius transformations elliptic parabolic and hyperbolic actions of sl symbol real number |
| title_sub | elliptic, parabolic and hyperbolic actions of SL[symbol]([real number]) |
| topic | Mobius transformations Möbius-Geometrie (DE-588)4750877-2 gnd Kleinsche Gruppe (DE-588)4164159-0 gnd Transformation (DE-588)4451062-7 gnd |
| topic_facet | Mobius transformations Möbius-Geometrie Kleinsche Gruppe Transformation |
| url | http://www.worldscientific.com/worldscibooks/10.1142/P835#t=toc |
| work_keys_str_mv | AT kisilvladimirv geometryofmobiustransformationsellipticparabolicandhyperbolicactionsofslsymbolrealnumber |