Minkowski Geometry

by A. C. Thompson

Overview

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.

Product Details

ISBN-13:	9780521404723
Publisher:	Cambridge University Press
Publication date:	06/28/1996
Series:	Encyclopedia of Mathematics and its Applications , #63
Pages:	368
Product dimensions:	6.46(w) x 9.53(h) x 0.98(d)

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; 9. Trigonometry; 10. Various numerical parameters.

Editorial Reviews

"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

From the Publisher

Explains a geometry that is non-Euclidean in a finite number of dimensions, different from elliptic and hyperbolic geometry and from the Minkowkian geometry of space-time, and in which a sphere is a general symmetric convex set and the Pythagorean theorem is invalid. The level is suitable for a senior undergraduate or beginning graduate familiar with the ideas of linear algebra and metric space topology. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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