Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(R) (With Dvd-Rom) - Image 1

£42.17

Imperial College Press Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(R) (With Dvd-Rom)

Name: Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(R) (With Dvd-Rom)
Brand: Imperial College Press
Price: 42.17 GBP
Availability: InStock

Mathematical Theory

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Description

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 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.

Product Specifications

Brand: Imperial College Press
Format: hardcover
ASIN: 1848168586
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Theory
Domain: Amazon UK
Release Date: 20 August 2012
Listed Since: 04 November 2011

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Imperial College Press Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(R) (With Dvd-Rom)

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