Euclidean and Non-Euclidean Geometry: An Analytic Approach
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.
1100946593
Euclidean and Non-Euclidean Geometry: An Analytic Approach
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.
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Euclidean and Non-Euclidean Geometry: An Analytic Approach

Euclidean and Non-Euclidean Geometry: An Analytic Approach

by Patrick J. Ryan
Euclidean and Non-Euclidean Geometry: An Analytic Approach

Euclidean and Non-Euclidean Geometry: An Analytic Approach

by Patrick J. Ryan

Overview

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.

Product Details

ISBN-13: 9780521276351
Publisher: Cambridge University Press
Publication date: 06/27/1986
Edition description: New Edition
Pages: 236
Product dimensions: 7.95(w) x 9.21(h) x 0.67(d)

Table of Contents

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.
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Science & Technology
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Mathematics
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Geometry - Euclidean & Projective
Geometry - General & Miscellaneous

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