This is an undergraduate textbook that reveals the intricacies of geometry. The approach used is that a geometry is a space together with a set of transformations of that space (as argued by Klein in his Erlangen programme). 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. 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.
Rezensionen / Stimmen
'This is a textbook that demonstrates the excitement and beauty of geometry ... richly illstrated and clearly written.' Extrait de L'Enseignement Mathematique ' ... this is a remarkable and nicely written introduction to classical geometry.' Zentralblatt MATH ' ... could form the basis of courses in geometry for mathematics undergraduates. It will also appeal to the general mathematical reader.' John Stone, The Times Higher Education Supplement
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises; 1 Tables, unspecified; 8 Halftones, unspecified; 614 Line drawings, unspecified
Maße
Höhe: 254 mm
Breite: 194 mm
Dicke: 29 mm
Gewicht
ISBN-13
978-0-521-59193-5 (9780521591935)
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Schweitzer Klassifikation
Autor*in
The Open University, Milton Keynes
The Open University, Milton Keynes
The Open University, Milton Keynes
Preface; Introduction; 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; Appendices; Index.
