Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(r) (With Dvd-rom)

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...