In this chapter, we study the group of transformations of E n generated by reflections in hyperplanes and inversions in spheres. It turns out that this group is isomorphic to the group of isometries of H n+1. This leads to a deeper understanding of hyperbolic geometry. In Sections 4.5 and 4.6, the conformai ball and upper half-space models of hyperbolic n-space are introduced. The chapter ends with a geometric analysis of the isometries of hyperbolic n-space.
KeywordsStereographic Projection Orthogonal Transformation Cross Ratio Linear Fractional Transformation Euclidean Sphere
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