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Author: Istv n Hargittai
Publisher: World Scientific
ISBN: 9789810206000
Category : Science
Languages : en
Pages : 594
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Book Description
Fivefold symmetry is common in flowers, fruits, molecules, logos, and buildings, but it is a forbidden symmetry in the world of crystals. A few years ago, the so-called quasicrystals were discovered displaying fivefold symmetry, and it caused a minirevolution in crystallography. There has been increased awareness of fivefold symmetry in all domains of human interest ever since. The present book brings together authors and ideas on a common theme from mathematics, the sciences, design, and anthropology to history, literature, and the arts. Its 29 chapters are an offering by scientists and humanists from 13 countries to a broad readership of professionals and laypersons about fivefold symmetry and the areas that are being bridged by this unique concept.
Author: Istv n Hargittai
Publisher: World Scientific
ISBN: 9789810206000
Category : Science
Languages : en
Pages : 594
Get Book Here
Book Description
Fivefold symmetry is common in flowers, fruits, molecules, logos, and buildings, but it is a forbidden symmetry in the world of crystals. A few years ago, the so-called quasicrystals were discovered displaying fivefold symmetry, and it caused a minirevolution in crystallography. There has been increased awareness of fivefold symmetry in all domains of human interest ever since. The present book brings together authors and ideas on a common theme from mathematics, the sciences, design, and anthropology to history, literature, and the arts. Its 29 chapters are an offering by scientists and humanists from 13 countries to a broad readership of professionals and laypersons about fivefold symmetry and the areas that are being bridged by this unique concept.
Author: R. A. Dunlap
Publisher: World Scientific
ISBN: 9789812386304
Category : Mathematics
Languages : en
Pages : 174
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Book Description
In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences. Contents: Basic Properties of the Golden Ratio; Geometric Problems in Two Dimensions; Geometric Problems in Three Dimensions; Fibonacci Numbers; Lucas Numbers and Generalized Fibonacci Numbers; Continued Fractions and Rational Approximants; Generalized Fibonacci Representation Theorems; Optimal Spacing and Search Algorithms; Commensurate and Incommensurate Projections; Penrose Tilings; Quasicrystallography; Biological Applications; Construction of the Regular Pentagon; The First 100 Fibonacci and Lucas Numbers; Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers. Readership: Applied mathematicians.
Author: Michael P. Marder
Publisher: John Wiley & Sons
ISBN: 0470949945
Category : Science
Languages : en
Pages : 985
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Book Description
Now updated—the leading single-volume introduction to solid state and soft condensed matter physics This Second Edition of the unified treatment of condensed matter physics keeps the best of the first, providing a basic foundation in the subject while addressing many recent discoveries. Comprehensive and authoritative, it consolidates the critical advances of the past fifty years, bringing together an exciting collection of new and classic topics, dozens of new figures, and new experimental data. This updated edition offers a thorough treatment of such basic topics as band theory, transport theory, and semiconductor physics, as well as more modern areas such as quasicrystals, dynamics of phase separation, granular materials, quantum dots, Berry phases, the quantum Hall effect, and Luttinger liquids. In addition to careful study of electron dynamics, electronics, and superconductivity, there is much material drawn from soft matter physics, including liquid crystals, polymers, and fluid dynamics. Provides frequent comparison of theory and experiment, both when they agree and when problems are still unsolved Incorporates many new images from experiments Provides end-of-chapter problems including computational exercises Includes more than fifty data tables and a detailed forty-page index Offers a solutions manual for instructors Featuring 370 figures and more than 1,000 recent and historically significant references, this volume serves as a valuable resource for graduate and undergraduate students in physics, physics professionals, engineers, applied mathematicians, materials scientists, and researchers in other fields who want to learn about the quantum and atomic underpinnings of materials science from a modern point of view.
Author: Eli Maor
Publisher: Princeton University Press
ISBN: 0691201129
Category : Mathematics
Languages : en
Pages : 184
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Book Description
A fascinating exploration of the pentagon and its role in various cultures The pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon’s wide-ranging history, no single book has explored the important role of this shape in various cultures, until now. Richly illustrated, Pentagons and Pentagrams offers a sweeping view of the five-sided polygon, revealing its intriguing geometric properties and its essential influence on a variety of fields. Traversing time, Eli Maor narrates vivid stories, both celebrated and unknown, about the pentagon and pentagram. He discusses the early Pythagoreans, who ascribed to the pentagon mythical attributes, adopted it as their emblem, and figured out its construction with a straightedge and compass. Maor looks at how a San Diego housewife uncovered four previously unknown types of pentagonal tilings, and how in 1982 a scientist’s discovery of fivefold symmetries in certain alloys caused an uproar in crystallography and led to a Nobel Prize. Maor also discusses the pentagon’s impact on many buildings, from medieval fortresses to the Pentagon in Washington, D.C. Eugen Jost’s superb illustrations provide sumptuous visual context, and the book’s puzzles and mazes offer fun challenges for readers, with solutions given in an appendix.
Author: Kristóf Fenyvesi
Publisher: Birkhäuser
ISBN: 3319572598
Category : Mathematics
Languages : en
Pages : 297
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Book Description
This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.
Author: COMAP
Publisher: Macmillan
ISBN: 1429226463
Category : Mathematics
Languages : en
Pages : 824
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Book Description
Contains complete solutions to odd-numbered problems in text.
Author: Mark Ladd
Publisher: Springer Science & Business Media
ISBN: 146143954X
Category : Science
Languages : en
Pages : 784
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Book Description
The advances in and applications of x-ray and neutron crystallography form the essence of this new edition of this classic textbook, while maintaining the overall plan of the book that has been well received in the academic community since the first edition in 1977. X-ray crystallography is a universal tool for studying molecular structure, and the complementary nature of neutron diffraction crystallography permits the location of atomic species in crystals which are not easily revealed by X-ray techniques alone, such as hydrogen atoms or other light atoms in the presence of heavier atoms. Thus, a chapter discussing the practice of neutron diffraction techniques, with examples, broadens the scope of the text in a highly desirable way. As with previous editions, the book contains problems to illustrate the work of each chapter, and detailed solutions are provided. Mathematical procedures related to the material of the main body of the book are not discussed in detail, but are quoted where needed with references to standard mathematical texts. To address the computational aspect of crystallography, the suite of computer programs from the fourth edition has been revised and expanded. The programs enable the reader to participate fully in many of the aspects of x-ray crystallography discussed in the book. In particular, the program system XRAY* is interactive, and enables the reader to follow through, at the monitor screen, the computational techniques involved in single-crystal structure determination, albeit in two dimensions, with the data sets provided. Exercises for students can be found in the book, and solutions are available to instructors.
Author: Vladimir A. Garanzha
Publisher: Springer Nature
ISBN: 3030767981
Category : Mathematics
Languages : en
Pages : 419
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Book Description
The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.
Author: C Janot
Publisher: World Scientific
ISBN: 9814548650
Category :
Languages : en
Pages : 856
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Book Description
These proceedings cover topics related to Quasicrystals, including tiling descriptions, high dimensional crystallography, structure studies, metallurgy and phase diagrams, and also properties with special emphasis on dynamics, electronic and mechanical behaviour. For the first time, materials made of metals only that behave as insulators are presented. For the first time also application focused research and processing of Quasicrystalline materials are addressed.Invited speakers: J Friedel, D Shechtman, M Baake, D Basov, C Berger, M de Boissieu, T Fujiwara, S Khanna, Y Meyer, S J Poon, C Sire, H Trebin, A P Tsai, M Widdom, M Wollgarten, Z Zhang.
Author: Alexei Ivlev
Publisher: World Scientific Publishing Company
ISBN: 9813108169
Category : Science
Languages : en
Pages : 337
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Book Description
Many fundamental issues in classical condensed matter physics can be addressed experimentally using systems of individually visible mesoscopic particles playing the role of “proxy atoms”. The interaction between such “atoms” is determined by the properties of the surrounding medium and/or by external tuning. The best-known examples of such experimental model systems are two different domains of soft matter — complex plasmas and colloidal dispersions.The major goal of this book — written by scientists representing both complex plasmas and colloidal dispersions — is to bring the two fields together. In the first part of the book the basic properties of the two systems are summarized, demonstrating huge conceptual and methodological overlap of the fields and emphasizing numerous cross-connections between them and their essential complementarity. This “introductory part” should serve to help each community in understanding the other field better. Simultaneously, this provides the necessary basis for the second part focused on particle-resolved studies of diverse generic phenomena in liquids and solids — all performed with complex plasmas and/or colloidal dispersions. The book is concluded with the discussion of critical open issues and fascinating perspectives of such interdisciplinary research.
