Euclidean and Non-Euclidean Geometry: An Analytic Approach

ISBN-13: 9780521276351 / Angielski / Miękka / 1986 / 236 str.

Patrick J. Ryan

Opis

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.

Recenzje

"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

Spis treści

Preface; Notation and special symbols; Historical introduction; 1. Plane Euclidean geometry; 2. Affine transformations in the Euclidean plane; 3. Finite groups of isometries of E2; 4. Geometry on the sphere; 5. The projective plane P2; 6. Distance geometry on P2; 7. The hyperbolic plane; Appendices; References; Index.