Geometry

This textbook demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen program: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case they carefully explain key results and discuss the relationship among geometries. This richly illustrated and clearly written text includes full solutions to over 200 problems and is suitable both for undergraduate courses on geometry and as a resource for self study. This Is A Textbook That Demonstrates The Excitement And Beauty Of Geometry. The Approach Is That Of Klein In His Erlangen Programme: A Geometry Is A Space Together With A Set Of Transformations Of That Space. The Authors Explore Various Geometries: Affine, Projective, Inversive, Non-euclidean And Spherical. In Each Case The Key Results Are Explained Carefully, And The Relationships Between The Geometries Are Discussed.--book Jacket. This Richly Illustrated And Clearly Written Text Includes Full Solutions To Over 200 Problems, And Is Suitable Both For Undergraduate Courses On Geometry And As A Resource For Self Study.--jacket. 0. Introduction: Geometry And Geometries -- 1. Conics -- 2. Affine Geometry -- 3. Projective Geometry: Lines -- 4. Projective Geometry: Conics -- 5. Inversive Geometry -- 6. Non-euclidean Geometry -- 7. Spherical Geometry -- 8. The Kleinian View Of Geometry -- App. 1. A Primer Of Group Theory -- App. 2. A Primer Of Vectors And Vector Spaces. David A. Brannan, Matthew F. Esplen, Jeremy J. Gray. Includes Index. "This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831"--