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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: Robert Glaser
Publisher: John Wiley & Sons
ISBN: 3527684204
Category : Science
Languages : en
Pages : 328
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Book Description
Written in a clear and understandable manner, this book provides a comprehensive, yet non-mathematical, treatment of the topic, covering the basic principles of symmetry and the important spectroscopic techniques used to probe molecular structure. The chapters are extensively illustrated and deal with such topics as symmetry elements, operations and descriptors, symmetry guidelines, high-fidelity pseudosymmetry, crystallographic symmetry, molecular gears, and experimental techniques, including X-ray crystallography and NMR spectroscopy. As an additional feature, 3D animations of most of the structures and molecules covered are available online at wiley.com. As a result, chemists learn how to understand and predict molecular structures and reactivity. Authored by a renowned expert with numerous publications and an excellent track record in research and teaching, this is a useful source for graduate students and researchers working in the field of organic synthesis, physical chemistry, biochemistry, and crystallography, while equally serving as supplementary reading for courses on stereochemistry, organic synthesis, or crystallography.
Author: Kim Williams
Publisher: Birkhäuser
ISBN: 3319001434
Category : Mathematics
Languages : en
Pages : 680
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Book Description
Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals. Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia.
Author: P J Steinhardt
Publisher: World Scientific Publishing Company
ISBN: 9813103841
Category : Science
Languages : en
Pages : 788
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Book Description
This book comprises an introductory lecture outlining the basic concepts and challenges in the field. This is followed by a collection of reprinted articles which are important in understanding the subject. The book will focus mainly on mathematical and physical foundations of the subject rather than experimental progress. By concentrating on theoretical topics, this volume has long-lasting as well as immediate value to physicists, crystallographers, metallurgists and mathematicians. Request Inspection Copy
Author: Consortium for Mathematics and Its Applications (U.S.)
Publisher: Macmillan
ISBN: 9780716759652
Category : Mathematics
Languages : en
Pages : 1000
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Book Description
For All Practical Purposes is the most effective and engaging textbook available for showing mathematics at work in areas with a direct impact on our lives (consumer products and advertising, politics, the economy, the Internet). It was the first, and remains the best, textbook for liberal arts students and for instructors who want to bring students the excitement of contemporary mathematical thinking and help their students think logically and critically. The new edition offers a number of changes designed to make the text more accessible than ever to a wider range of students and instructors.
Author: M.J. Yacamán
Publisher: Elsevier
ISBN: 0444599142
Category : Science
Languages : en
Pages : 248
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Book Description
The discovery of five-fold diffraction symmetry by D. Schechtman in 1985 shocked crystallography to its roots. Incommensurable modulation of a crystal changes former identical unit cells into different ones. This radical revolution has given rise to the study of an entirely new class of matter, the quasicrystalline materials. The study of these quasi-periodic crystals brings a unique elucidation of the fundaments of crystallography and the relationship between lattice structure and macroscopic properties. This book covers the transitions between the crystalline and the quasicrystalline state. A thorough understanding of the transition from quasiperiodic to periodic lattices is essential in order to investigate the uniqueness of quasicrystals. In this well-written volume, an overview is given of the most important problems in quasicrystallography today. Leading experts provide insight into recent experimental advances achieved by studying the phase transitions between crystalline and quasicrystalline states. In the theoretical chapters one is introduced to the depth of insight into the nature of crystallography which has arisen through a rigorous understanding of the quasicrystal structure. This book is an essential source of reference for crystallographers, crystal growers and solid state physicists working in the field.
Author: Jay Bonner
Publisher: Springer
ISBN: 1441902171
Category : Mathematics
Languages : en
Pages : 616
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Book Description
The main focus of this unique book is an in-depth examination of the polygonal technique; the primary method used by master artists of the past in creating Islamic geometric patterns. The author details the design methodology responsible for this all-but-lost art form and presents evidence for its use from the historical record, both of which are vital contributions to the understanding of this ornamental tradition. Additionally, the author examines the historical development of Islamic geometric patterns, the significance of geometric design within the broader context of Islamic ornament as a whole, the formative role that geometry plays throughout the Islamic ornamental arts (including calligraphy, the floral idiom, dome decoration, geometric patterns, and more), and the underexamined question of pattern classification. Featuring over 600 beautiful color images, Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Con struction is a valuable addition to the literature of Islamic art, architecture and geometric patterns. This book is ideal for students and scholars of geometry, the history of mathematics, and the history of Islamic art, architecture, and culture. In addition, artists, designers, craftspeople, and architects will all find this book an exceptionally informative and useful asset in their fields. Jay Bonner is an architectural ornamentalist and unaffiliated scholar of Islamic geometric design. He received his MDes from the Royal College of Art in London (1983). He has contributed ornamental designs for many international architectural projects, including the expansion of both the al-Masjid al-Haram (Grand Mosque) in Mecca, and the al-Masjid an Nawabi (Prophet’s Mosque) in Medina, as well the Tomb of Sheikh Hujwiri in Lahore, and the Ismaili Centre in London – to name but a few. He is committed to the revitalization of Islamic geometric design through the teaching of traditional methodological practices. To this end, in addition to publishing, Jay Bonner has lectured and taught design seminars at many universities and conferences in North America, Europe, North Africa and Asia.
Author: Argonne National Laboratory
Publisher:
ISBN:
Category : Engineering experiment stations
Languages : en
Pages : 40
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Book Description
Author: Perla Balbuena
Publisher: Elsevier
ISBN: 0080466834
Category : Science
Languages : en
Pages : 329
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Book Description
Over the past few decades, several approaches have been developed for designing nano-structured or molecularly-structured materials. These advances have revolutionized practically all fields of science and engineering, providing an additional design variable, the feature size of the nano-structures, which can be tailored to provide new materials with very special characteristics. Nanomaterials: Design and Simulation explores the role that such advances have made toward a rational design of nanostructures and covers a variety of methods from ab initio electronic structure techniques, ab initio molecular dynamics, to classical molecular dynamics, also being complemented by coarse-graining and continuum methods. Also included is an overview of how the development of these computational tools has enabled the possibility of exploring nanoscopic details and using such information for the prediction of physical and chemical properties that are not always possible to be obtained experimentally.* Provides an overview of approaches that have been developed for designing nano-structured or molecularly-structured materials.* This volume covers several aspects of the simulation and design of nanomaterials analyzed by a selected group of active researchers in the field. * Looks at how the advancement of computational tools have enabled nanoscopic prediction of physical and chemical properties
