Geometry of Mčobius TransformationsGeometry of Mčobius Transformations
Elliptic, Parabolic and Hyperbolic Actions of SL2, (R)
Title rated 0 out of 5 stars, based on 0 ratings(0 ratings)
eBook, 2012
Current format, eBook, 2012, , All copies in use.eBook, 2012
Current format, eBook, 2012, , All copies in use. Offered in 0 more formatsThis 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.
Title availability
About
Details
Publication
- London, UK : Imperial College Press ; Singapore : World Scientific, 2012.
Opinion
More from the community
Community lists featuring this title
There are no community lists featuring this title
Community contributions
Community quotations are the opinions of contributing users. These quotations do not represent the opinions of Whistler Public Library.
There are no quotations from this title
Community quotations are the opinions of contributing users. These quotations do not represent the opinions of Whistler Public Library.
There are no quotations from this title
From the community