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Bodies of Constant Width
An Introduction to Convex Geometry with Applications
Langbeschreibung
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.
Hauptbeschreibung
Provides an extensive exploration of constant width bodies
Inhaltsverzeichnis
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.
Horst Martini obtained his PhD in Dresden/Germany (1984) and defended his habilitation at the Schiller University in Jena (1988). Since 1993 he is Full Professor for Mathematics at the University of Technology in Chemnitz, Germany (Chair of Geometry). He received a von Humboldt Scholarship in 1990, and an honorary professorship from the Harbin University of Science and Technology (China) in 2015. His main mathematical interests are focused on convex and discrete geometry, the geometry of finite dimensional real Banach spaces, and combinatorics.
ISBN-13:
9783030038663
Veröffentl:
2019
Erscheinungsdatum:
28.03.2019
Seiten:
500
Autor:
Horst Martini
Gewicht:
1241 g
Format:
260x183x31 mm
Sprache:
Englisch