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Geometry of möbius transformations ...

Kisil, Vladimir V.

Geometry of möbius transformations = elliptic, parabolic and hyperbolic actions of SL2, (R) /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Geometry of möbius transformations/ Vladimir V. Kisil.
其他題名:	elliptic, parabolic and hyperbolic actions of SL2, (R) /
作者:	Kisil, Vladimir V.
出版者:	London, UK :Imperial College Press ; : 2012.,
面頁冊數:	1 online resource (xiv, 192 pages) :illustrations :
標題:	Möbius transformations. -
電子資源:	http://www.worldscientific.com/worldscibooks/10.1142/P835#t=toc
ISBN:	9781848168596 (electronic bk.)

Geometry of möbius transformations = elliptic, parabolic and hyperbolic actions of SL2, (R) /
Kisil, Vladimir V.

Geometry of möbius transformationselliptic, parabolic and hyperbolic actions of SL2, (R) /[electronic resource] :Vladimir V. Kisil. - London, UK :Imperial College Press ;2012. - 1 online resource (xiv, 192 pages) :illustrations

Includes bibliographical references and index.

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.

ISBN: 9781848168596 (electronic bk.)

Standard No.: 9786613784193Subjects--Topical Terms:

943632
Möbius transformations.

LC Class. No.: QA601 / .K57 2012eb

Dewey Class. No.: 516.1

Geometry of möbius transformations = elliptic, parabolic and hyperbolic actions of SL2, (R) /
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100 1 $a Kisil, Vladimir V. $3 943631
245 1 0 $a Geometry of möbius transformations $h [electronic resource] : $b elliptic, parabolic and hyperbolic actions of SL2, (R) / $c Vladimir V. Kisil.
260 $a London, UK : $b Imperial College Press ; $a Singapore : $b World Scientific, $c 2012.
300 $a 1 online resource (xiv, 192 pages) : $b illustrations
504 $a Includes bibliographical references and index.
520 $a 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.
588 $a Description based on print version record.
650 0 $a Möbius transformations. $3 943632
856 4 0 $u http://www.worldscientific.com/worldscibooks/10.1142/P835#t=toc

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