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

Geometry of Möbius Transformations: Elliptic, Parabolic and Hyperbolic Actions of SL₂ (R)

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 E...