
Bodies of Constant Width
An Introduction to Convex Geometry with Applications
Birkhäuser (Publisher)
Published on 13. April 2019
Book
Hardback
XI, 486 pages
978-3-030-03866-3 (ISBN)
Description
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 Fourier series, spherical integration, and other related methods)
- Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.)
- Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics)
- The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.)
- Technical applications, such as film projectors, the square-hole drill, and rotary engines
More details
Product info
Book
Edition
2018
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
College/higher education
Illustrations
131 s/w Abbildungen, 24 farbige Tabellen, 32 farbige Abbildungen
129 schwarz-weiße und 29 farbige Abbildungen, 24 farbige Tabellen, Bibliographie
Dimensions
Height: 260 mm
Width: 183 mm
Thickness: 31 mm
Weight
1241 gr
ISBN-13
978-3-030-03866-3 (9783030038663)
DOI
10.1007/978-3-030-03868-7
Schweitzer Classification
Other editions
Additional editions

Horst Martini | Luis Montejano | Déborah Oliveros
Bodies of Constant Width
An Introduction to Convex Geometry with Applications
E-Book
03/2019
Birkhäuser
€96.29
Available for download
Persons
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.
Luis Montejano had graduate studies at MIT and the University of Utah, and he received his PhD in 1980. As a postdoc, he was member of the Institute for Advanced Studies, Princeton, and in 1990 he obtained a von Humboldt Scholarship in Heidelberg. He is Professor at the National University of Mexico, Campus Querétaro. His main mathematical interests refer to applications of topology to discrete and convex geometry.
Deborah Oliveros studied mathematics at the National University of Mexico UNAM, and she obtained her PhD in 1997. After that she got a postdoctoral position at the University of Calgary, Canada, where she stayed for several years. She is now Professor at the National University of Mexico, Campus Juriquilla, and her main mathematical interests are convex and abstract polytopes, discrete geometry, and convexity.
Content
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.