Geometries on Surfaces
Geometries on Surfaces
Günter Steinke, University of Canterbury, Christchurch, New Zealand
$191.00
USDOne century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have included detailed sections on what is known as well as outlining problems that remain to be solved. There are sections on classical geometries, methods for constructing non-classical geometries and classifications and characterizations of geometries. This work is related to a host of other fields including approximation, convexity, differential geometry topology and many more. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas outlined above.
- Comprehensive survey of geometries on planes
- Can be read as both an introduction and a reference
- Contains sections on future research directions
Reviews & endorsements
"This book mainly concerns geometries with point sets that form some sort of surface (e.g. a plane, a sphere, a torus, a cylinder) and line sets of a general nature that validate certain standard sets of incidence axioms.... Altogether well designed, quite suitable for browsing, and accessible to undergraduates, this book will form a vital supplement to courses in the foundations of geometry. General readers; lower-division undergraduates through faculty." Choice
"...a carefully written introduction to the subject of topological geometries on surfaces, with many illustrations, motivations, and examples." Mathematical Reviews
Product details
January 2002Hardback
9780521660587
514 pages
234 × 156 × 29 mm
0.89kg
90 b/w illus.
Available
Table of Contents
- 1. Geometries for pedestrians
- 2. Flat linear spaces
- 3. Spherical circle planes
- 4. Toroidal circle planes
- 5. Cylindrical circle planes
- 6. Generalized quadrangles
- 7. Tubular circle planes
- Appendices.
