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Author : Rachel Griffith,Stephen Redding,John Van Reenen
Publisher : Unknown
Page : 88 pages
File Size : 51,6 Mb
Release : 2000
Category : Economics
ISBN : UVA:X006091537
Author : Imre Bárány,Károly Jr. Böröczky,Gábor Fejes Tóth,Janos Pach
Publisher : Springer
Page : 367 pages
File Size : 44,9 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9783642414985
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.
Author : C. M. Campbell,C. W. Parker,M. R. Quick,E. F. Robertson,C. M. Roney-Dougal
Publisher : Cambridge University Press
Page : 510 pages
File Size : 49,5 Mb
Release : 2019-04-11
Category : Mathematics
ISBN : 9781108728744
These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.
Author : Harold S.M. Coxeter,William O. J. Moser
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 43,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662219430
When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i.e.' .subgroups of es), the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-142) deal with groups of low order, finite and infinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute for a more extensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer.
Author : Harold Scott Macdonald Coxeter,William O. J. Moser
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 48,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662257395
When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i. e., subgroups of e ), the reader cannot do better than consult the 8 tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-143) deal with groups of low order, finiteandinfinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute foramoreextensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer. There is also a topological method (Chapter 3), suitable not only for groups of low order but also for some infinite groups. This involves choosing a set of generators, constructing a certain graph (the Cayley diagram or DEHNsehe Gruppenbild), and embedding the graph into a surface. Cases in which the surface is a sphere or a plane are described in Chapter 4, where we obtain algebraically, and verify topologically, an abstract definition for each of the 17 space groups of two-dimensional crystallography.
Author : Liu Yanpei
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 43,8 Mb
Release : 2000-08-31
Category : Mathematics
ISBN : 0792355997
Combinatorics as a branch of mathematics studies the arts of counting. Enumeration occupies the foundation of combinatorics with a large range of applications not only in mathematics itself but also in many other disciplines. It is too broad a task to write a book to show the deep development in every corner from this aspect. This monograph is intended to provide a unified theory for those related to the enumeration of maps. For enumerating maps the first thing we have to know is the sym metry of a map. Or in other words, we have to know its automorphism group. In general, this is an interesting, complicated, and difficult problem. In order to do this, the first problem we meet is how to make a map considered without symmetry. Since the beginning of sixties when Tutte found a way of rooting on a map, the problem has been solved. This forms the basis of the enumerative theory of maps. As soon as the problem without considering the symmetry is solved for one kind of map, the general problem with symmetry can always, in principle, be solved from what we have known about the automorphism of a polyhedron, a synonym for a map, which can be determined efficiently according to another monograph of the present author [Liu58].
Author : B.H. Arnold
Publisher : Courier Corporation
Page : 192 pages
File Size : 47,9 Mb
Release : 2015-02-23
Category : Mathematics
ISBN : 9780486275765
Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.
Author : Jay Kappraff
Publisher : World Scientific
Page : 528 pages
File Size : 47,8 Mb
Release : 2001
Category : Science
ISBN : 9812811397
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in OC Mathematics, Chemistry, and Astronomy OCo Professional and ReferenceOCO in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. Contents: Proportion in Architecture; Similarity; The Golden Mean; Graphs; Tilings with Polygons; Two-Dimensional Networks and Lattices; Polyhedra: Platonic Solids; Transformation of the Platonic Solids I; Transformation of the Platonic Solids II; Polyhedra: Space Filling; Isometries and Mirrors; Symmetry of the Plane. Readership: Polytechnic students, architects, designers, mathematicians and general readers."
Author : Guillaume Damiand,Pascal Lienhardt
Publisher : CRC Press
Page : 407 pages
File Size : 42,8 Mb
Release : 2014-09-19
Category : Computers
ISBN : 9781482206524
A Versatile Framework for Handling Subdivided Geometric Objects Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing gathers important ideas related to combinatorial maps and explains how the maps are applied in geometric modeling and image processing. It focuses on two subclasses of combinatorial maps: n-Gmaps and n-maps. Suitable for researchers and graduate students in geometric modeling, computational and discrete geometry, computer graphics, and image processing and analysis, the book presents the data structures, operations, and algorithms that are useful in handling subdivided geometric objects. It shows how to study data structures for the explicit representation of subdivided geometric objects and describes operations for handling the structures. The book also illustrates results of the design of data structures and operations.
Author : David W. Barnette
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 42,6 Mb
Release : 1984-03-01
Category : Mathematics
ISBN : 9781470457174
Author : Oleg N. Karpenkov
Publisher : Springer Nature
Page : 462 pages
File Size : 54,8 Mb
Release : 2022-05-28
Category : Mathematics
ISBN : 9783662652770
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Author : Asaf Nachmias
Publisher : Springer Nature
Page : 120 pages
File Size : 43,9 Mb
Release : 2019-10-04
Category : Mathematics
ISBN : 9783030279684
This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.
Author : Jay Kappraff
Publisher : World Scientific
Page : 520 pages
File Size : 45,7 Mb
Release : 2001-11-28
Category : Mathematics
ISBN : 9789814491327
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in “Mathematics, Chemistry, and Astronomy — Professional and Reference” in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture and design, tilings and patterns, polyhedra, and symmetry. The book presents both theory and practice and has more than 750 illustrations. It is suitable for research in a variety of fields and as an aid to teaching a course in the mathematics of design. It has been influential in stimulating the burgeoning interest in the relationship between mathematics and design. In the second edition there are five new sections, supplementary, as well as a new preface describing the advances in design science since the publication of the first edition. Contents: Proportion in ArchitectureSimilarityThe Golden MeanGraphsTilings with PolygonsTwo-Dimensional Networks and LatticesPolyhedra: Platonic SolidsTransformation of the Platonic Solids ITransformation of the Platonic Solids IIPolyhedra: Space FillingIsometries and MirrorsSymmetry of the Plane Readership: Polytechnic students, architects, designers, mathematicians and general readers. Keywords:Design Science;Art;Architecture;Geometry;Polyhedra;Tilings;Graph Theory;Symmetry;Proportion;Golden MeanReviews: “This book, on the mathematics of natural and artful form, is a lively new entrant to the small shelf of those fine works.” Scientific American “If I had only one book in my library to which I refer for mathematics questions in art and architecture, this would be the one.” Nexus Network Journal “A worthy volume rediscovers the golden mean for readers in the postgeometry generation.” BYTE “… Kappraff's book is nothing less than the first textbook of design science.”Bulletin of the Buckminster Fuller Institute “This is no less than an early and strong move toward implementing Buckminster Fuller's call for a Comprehensive Anticipatory Design Science. Even a less-than-rigorous reading will convince you that something important is being presented here.” Whole Earth Review “For the visually oriented person with a hunger to understand pattern, Connections can be a bridge to a new world.” American Journal of Physics “A spectacular presentation of design science — ‘the grammar of space’ — that explores with rich details instances of similarity, proportion, tilings, graphs, lattices, polyhedra, isometries, and symmetry in art, architecture, engineering, and science. Punctuated with exercises and problems (thus making the monograph useful as a course or seminar text); illustrated with over 200 figures; supported by an extensive multi-disciplinary bibliography that is well-referenced to the text. A superb option for interdisciplinary seminars.” American Mathematical Monthly
Author : Parker CLEAVELAND
Publisher : Unknown
Page : 510 pages
File Size : 48,6 Mb
Release : 1822
Category : Electronic
ISBN : BL:A0024272725
Author : Joel Katz
Publisher : John Wiley & Sons
Page : 226 pages
File Size : 54,9 Mb
Release : 2012-08-20
Category : Design
ISBN : 9781118420096
"The book itself is a diagram of clarification, containing hundreds of examples of work by those who favor the communication of information over style and academic postulation—and those who don't. Many blurbs such as this are written without a thorough reading of the book. Not so in this case. I read it and love it. I suggest you do the same." —Richard Saul Wurman "This handsome, clearly organized book is itself a prime example of the effective presentation of complex visual information." —eg magazine "It is a dream book, we were waiting for...on the field of information. On top of the incredible amount of presented knowledge this is also a beautifully designed piece, very easy to follow..." —Krzysztof Lenk, author of Mapping Websites: Digital Media Design "Making complicated information understandable is becoming the crucial task facing designers in the 21st century. With Designing Information, Joel Katz has created what will surely be an indispensable textbook on the subject." —Michael Bierut "Having had the pleasure of a sneak preview, I can only say that this is a magnificent achievement: a combination of intelligent text, fascinating insights and - oh yes - graphics. Congratulations to Joel." —Judith Harris, author of Pompeii Awakened: A Story of Rediscovery Designing Information shows designers in all fields - from user-interface design to architecture and engineering - how to design complex data and information for meaning, relevance, and clarity. Written by a worldwide authority on the visualization of complex information, this full-color, heavily illustrated guide provides real-life problems and examples as well as hypothetical and historical examples, demonstrating the conceptual and pragmatic aspects of human factors-driven information design. Both successful and failed design examples are included to help readers understand the principles under discussion.