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This is a comprehensive treatment of Minkowski geometry. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterizations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces--a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere.Read more
- Comprehensive, self-contained treatment
- Many attractive illustrations
Reviews & endorsements
"The author's writing is clear, scholarly and elegant. Each chapter opens with a summary and detailed text follows. An extensive commentary with historical notes closes the chapter. There is a comprehensive bibliography with entries as late as 1995. The printing is accurate and clear as are the many figures, some of which are beautiful." W.J. Firey, Mathematical Reviews
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- Date Published: June 1996
- format: Hardback
- isbn: 9780521404723
- length: 368 pages
- dimensions: 242 x 164 x 25 mm
- weight: 0.718kg
- contains: 50 b/w illus.
- availability: Available
Table of Contents
1. The algebraic properties of linear spaces and of convex sets
2. Norms and norm topologies
3. Convex bodies
4. Comparisons and contrasts with Euclidean space
5. Two dimensional Minkowski spaces
6. The concept of area and content
7. Special properties of the Holmes-Thompson definition
8. Special properties of the Busemann definition
10. Various numerical parameters.
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