Minkoski Geometry [Hardcover]

The first comprehensive treatment of Minkowski geometry since the 1940'sMinkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not uniform in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940's, with chapters on fundamental metric and topological properties, the theory of area and volume in normed spaces (a fascinating geometrical interplay among the various roles of the ball in Euclidean space), trigonometry and differential geometry. The book will appeal to students and researchers interested in geometry and analysis.Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not uniform in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940's, with chapters on fundamental metric and topological properties, the theory of area and volume in normed spaces (a fascinating geometrical interplay among the various roles of the ball in Euclidean space), trigonometry and differential geometry. The book will appeal to students and researchers interested in geometry and analysis.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.1. The algebraic properties of linear spaces and of convex sets; 2. Norms and norm topologies; 3. Convex bodies; 4. CompalÃ{