Euclidean and Non-Euclidean Geometry: An Analytic Approach

Description

This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic. The primary purpose is to acquaint the reader with the classical results of plane Euclidean and nonEuclidean geometry, congruence theorems, concurrence theorems, classification of isometries, angle addition and trigonometrical formulae. However, the book not only provides students with facts about and an understanding of the structure of the classical geometries, but also with an arsenal of computational techniques for geometrical investigations. The aim is to link classical and modern geometry to prepare students for further study and research in group theory, Lie groups, differential geometry, topology, and mathematical physics. The book is intended primarily for undergraduate mathematics students who have acquired the ability to formulate mathematical propositions precisely and to construct and understand mathematical arguments. Some familiarity with linear algebra and basic mathematical functions is assumed, though all the necessary background material is included in the appendices.

"An elegant geometry text...the whole very crisply printed and illustrated. Good exercises and helpful references." SciTech Book News "...a thoughtful, carefully crafted textbook..." Science Books & Films "The exposition is lucid; the body of the text and exercises are thoughtfully organized...The book should be brought to the attention of instructors wishing for a fresh outlook..." American Scientist "In his introduction the author expresses the hope that he can instill good working attitudes that will help students go on to research in group theory, Lie groups, differential geometry and topology. The naturalness and sophistication of his development go far to fulfilling his aim...The book is produced to a very high standard. Both graphics and text are exceptionally clear." The Mathematical Gazette