Non-Euclidean geometry

About “Non-Euclidean geometry”

The book presents non-Euclidean geometries in two and three dimensions as specializations of real projective geometry, using a synthetic approach based on axioms concerning points, lines, planes, incidence, order, and continuity, without reference to distance or angle measurement. It develops the subject through the introduction of homogeneous coordinates and colineations, leading to elliptic and hyperbolic geometries via elliptic or hyperbolic polarity, with a final section on inversive distance added in the sixth edition.