Geometries on Surfaces
Geometries on Surfaces
Günter Steinke, University of Canterbury, Christchurch, New Zealand
$191.00
USDThe projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, topology, the theory of Lie groups, and many more. The authors detail these connections, some of which are well-known, but many much less so. Acting both as a reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact.
- 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
May 2012Adobe eBook Reader
9781139238939
0 pages
0kg
90 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
