Brannan, D. A. creator Esplen, Matthew F. Gray, Jeremy 1947- text bibliography enk Cambridge New York Cambridge University Press 2012 2nd ed. monographic eng

print

xiv, 587 p. : ill. ; 25 cm. "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"-- Machine generated contents note: Preface; Introduction: geometry and geometries; 1. Conics; 2. Affine geometry; 3. Projective geometry: lines; 4. Projective geometry: conics; 5. Inversive geometry; 6. Hyperbolic geometry: the disc model; 7. Elliptic geometry: the spherical model; 8. The Kleinian view of geometry; Special symbols; Further reading; Appendix 1. A primer of group theory; Appendix 2. A primer of vectors and vector spaces; Appendix 3. Solutions to the problems; Index. David A. Brannan, Matthew F. Esplen, Jeremy J. Gray. Includes bibliographical resources and index. Geometry MATHEMATICS / Topology QA445 .B688 2012 516 BRA/G MAT038000 9781107627888 2011030683 http://assets.cambridge.org/97811076/47831/cover/9781107647831.jpg http://assets.cambridge.org/97811076/47831/cover/9781107647831.jpg DLC 110725 20210702115008.0 16887664