Bodies Of Constant Width

Author : Horst Martini
Publisher : Springer
ISBN 13 : 3030038688
Total Pages : 486 pages
Book Rating : 4.87/5 ( download)

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Download or read book Bodies of Constant Width written by Horst Martini and published by Springer. This book was released on 2019-03-16 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.

Author : John Bryant
Publisher : Princeton University Press
ISBN 13 : 1400837952
Total Pages : 320 pages
Book Rating : 4.53/5 ( download)

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Download or read book How Round Is Your Circle? written by John Bryant and published by Princeton University Press. This book was released on 2011-02-28 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun. John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.

Author : GRUBER
Publisher : Birkhäuser
ISBN 13 : 3034858582
Total Pages : 419 pages
Book Rating : 4.88/5 ( download)

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Download or read book Convexity and Its Applications written by GRUBER and published by Birkhäuser. This book was released on 2013-11-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.

Author : Silouanos Brazitikos
Publisher : American Mathematical Soc.
ISBN 13 : 1470414562
Total Pages : 618 pages
Book Rating : 4.66/5 ( download)

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Download or read book Geometry of Isotropic Convex Bodies written by Silouanos Brazitikos and published by American Mathematical Soc.. This book was released on 2014-04-24 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture. This book provides a self-contained and up to date account of the progress that has been made in the last fifteen years.

Author : Gerd Fischer
Publisher : Informatica International, Incorporated
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.74/5 ( download)

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Download or read book Mathematical models written by Gerd Fischer and published by Informatica International, Incorporated. This book was released on 1986 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Shaun Gallagher
Publisher : Clarendon Press
ISBN 13 : 0191622575
Total Pages : 295 pages
Book Rating : 4.71/5 ( download)

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Download or read book How the Body Shapes the Mind written by Shaun Gallagher and published by Clarendon Press. This book was released on 2006-10-12 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: How the Body Shapes the Mind is an interdisciplinary work that addresses philosophical questions by appealing to evidence found in experimental psychology, neuroscience, studies of pathologies, and developmental psychology. There is a growing consensus across these disciplines that the contribution of embodiment to cognition is inescapable. Because this insight has been developed across a variety of disciplines, however, there is still a need to develop a common vocabulary that is capable of integrating discussions of brain mechanisms in neuroscience, behavioural expressions in psychology, design concerns in artificial intelligence and robotics, and debates about embodied experience in the phenomenology and philosophy of mind. Shaun Gallagher's book aims to contribute to the formulation of that common vocabulary and to develop a conceptual framework that will avoid both the overly reductionistic approaches that explain everything in terms of bottom-up neuronal mechanisms, and inflationistic approaches that explain everything in terms of Cartesian, top-down cognitive states. Gallagher pursues two basic sets of questions. The first set consists of questions about the phenomenal aspects of the structure of experience, and specifically the relatively regular and constant features that we find in the content of our experience. If throughout conscious experience there is a constant reference to one's own body, even if this is a recessive or marginal awareness, then that reference constitutes a structural feature of the phenomenal field of consciousness, part of a framework that is likely to determine or influence all other aspects of experience. The second set of questions concerns aspects of the structure of experience that are more hidden, those that may be more difficult to get at because they happen before we know it. They do not normally enter into the content of experience in an explicit way, and are often inaccessible to reflective consciousness. To what extent, and in what ways, are consciousness and cognitive processes, which include experiences related to perception, memory, imagination, belief, judgement, and so forth, shaped or structured by the fact that they are embodied in this way?

Author : Peter Ring
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212065
Total Pages : 742 pages
Book Rating : 4.6X/5 ( download)

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Download or read book The Nuclear Many-Body Problem written by Peter Ring and published by Springer Science & Business Media. This book was released on 2004-03-25 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Study Edition

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.94/5 ( download)

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Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Author : Giorgio Talenti
Publisher : CRC Press
ISBN 13 : 9780824796983
Total Pages : 392 pages
Book Rating : 4.85/5 ( download)

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Download or read book partial differential equations and applications written by Giorgio Talenti and published by CRC Press. This book was released on 1996-01-16 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.

Author : Peter Brass
Publisher : Springer Science & Business Media
ISBN 13 : 0387238158
Total Pages : 507 pages
Book Rating : 4.59/5 ( download)

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Download or read book Research Problems in Discrete Geometry written by Peter Brass and published by Springer Science & Business Media. This book was released on 2006-06-19 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.