Foundations of Plane Geometry

For undergraduate level courses in Geometry. Ideal for students who may have little previous experience with abstraction and proof, this text provides a rigorous and unified - yet straightforward and accessible - exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme - the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes - with a leisurely development that allows ample time for students' 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. *Focuses on one main topic - The axiomatic development of the absolute plane - which is pursued through a classification into Euclidean, hyperbolic, and spherical planes. *The theme of simultaneous study of different types of Plane geometry. *Presents the axioms for absolute plane geometry gradually. *Forces students to consider familiar words in a new light.
*Unique approach to the standard sets of axioms. *States and discusses the Ruler and Protractor Axioms (commonly used in secondary school geometry texts) as theorems. *Informal chapter on logic. *10 to 20 exercises varied in length and difficulty, at the end of each chapter.