Bodies of Constant Width : An Introduction to Convex Geometry with Applications. 1st ed. 2019

種類:

電子ブック

責任表示:

by Horst Martini, Luis Montejano, Déborah Oliveros

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2019

著者名:

• Martini, Horst.
• Montejano, Luis.
• Oliveros, Déborah.
• SpringerLink (Online service)

ISBN:

9783030038687 [3030038688]    

注記:

Introduction -- Convex Geometry -- Basic Properties of Bodies of Constant Width -- Figures of Constant Width -- Systems of Lines in the Plane -- Spindle Convexity -- Complete and Reduced Convex Bodies -- Examples and Constructions -- Sections of Bodies of Constant Width -- Bodies of Constant Width in Mikowski Spaces -- Bodies of Constant Width in Differential Geometry -- Mixed Volumes -- Bodies of Constant Width in Analysis -- Geometric Inequalities -- Bodies of Constant Width in Discrete Geometry -- Bodies of Constant Width in Topology -- Concepts Related to Constant Width -- Bodies of Constant Width in Art, Design, and Engineering.
This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourie

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