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.
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.
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 345 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.
Download or read book Bodies of Constant Width in Reimannian Manifolds and Spaces of Constant Curvature written by Boris V. Dekster and published by . This book was released on 1991 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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 519 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?
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
Download or read book Convex Bodies The Brunn Minkowski Theory written by Rolf Schneider and published by Cambridge University Press. This book was released on 2014 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Download or read book Human Dimension and Interior Space written by Julius Panero and published by Watson-Guptill. This book was released on 2014-01-21 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of human body measurements on a comparative basis is known as anthropometrics. Its applicability to the design process is seen in the physical fit, or interface, between the human body and the various components of interior space. Human Dimension and Interior Space is the first major anthropometrically based reference book of design standards for use by all those involved with the physical planning and detailing of interiors, including interior designers, architects, furniture designers, builders, industrial designers, and students of design. The use of anthropometric data, although no substitute for good design or sound professional judgment should be viewed as one of the many tools required in the design process. This comprehensive overview of anthropometrics consists of three parts. The first part deals with the theory and application of anthropometrics and includes a special section dealing with physically disabled and elderly people. It provides the designer with the fundamentals of anthropometrics and a basic understanding of how interior design standards are established. The second part contains easy-to-read, illustrated anthropometric tables, which provide the most current data available on human body size, organized by age and percentile groupings. Also included is data relative to the range of joint motion and body sizes of children. The third part contains hundreds of dimensioned drawings, illustrating in plan and section the proper anthropometrically based relationship between user and space. The types of spaces range from residential and commercial to recreational and institutional, and all dimensions include metric conversions. In the Epilogue, the authors challenge the interior design profession, the building industry, and the furniture manufacturer to seriously explore the problem of adjustability in design. They expose the fallacy of designing to accommodate the so-called average man, who, in fact, does not exist. Using government data, including studies prepared by Dr. Howard Stoudt, Dr. Albert Damon, and Dr. Ross McFarland, formerly of the Harvard School of Public Health, and Jean Roberts of the U.S. Public Health Service, Panero and Zelnik have devised a system of interior design reference standards, easily understood through a series of charts and situation drawings. With Human Dimension and Interior Space, these standards are now accessible to all designers of interior environments.
Download or read book Active Calculus 2018 written by Matthew Boelkins and published by Createspace Independent Publishing Platform. This book was released on 2018-08-13 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.
Download or read book Many Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and published by Oxford University Press. This book was released on 2004-09-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
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.
Download or read book Double Normals Characterize Bodies of Constant Width in Riemannian Manifolds written by Boris V. Dekster and published by . This book was released on 1993 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Convexity from the Geometric Point of View written by Vitor Balestro and published by Springer Nature. This book was released on with total page 1195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convexity written by H. G. Eggleston and published by CUP Archive. This book was released on 1958 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This account of convexity includes the basic properties of convex sets in Euclidean space and their applications, the theory of convex functions and an outline of the results of transformations and combinations of convex sets. It will be useful for those concerned with the many applications of convexity in economics, the theory of games, the theory of functions, topology, geometry and the theory of numbers.
