Foundations of Plane Geometry Author:Harvey I. Blau Ideal for users who may have little previous experience with abstraction and proof, this book provides a rigorous and unifiedyet straightforward and accessibleexposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended themethe study of a gen... more »eralized absolute plane from axioms through classification into the three fundamental classical planeswith a leisurely development that allows ample time for mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular. Focus on one main topicThe axiomatic development of the absolute planewhich is pursued through a classification into Euclidean, hyperbolic, and spherical planes. Presents specific models such as the sphere, the Klein-Betrami hyperbolic model, and the gap plane. Gradually presents axioms for absolute plane geometry.« less