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Creating Symmetry

Author: Frank A. Farris

Publisher: Princeton University Press

Published: 2015-06-02

Total Pages: 247

ISBN-13: 1400865670

A step-by-step illustrated introduction to the astounding mathematics of symmetry This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks—a sort of potato-stamp method—Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

Dynamic Symmetry: The Greek Vase

Author: Jay Hambidge

Publisher: Legare Street Press

Published: 2022-10-27

Total Pages: 0

ISBN-13: 9781015651043

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Dynamic Symmetry

Author: Tavis Leaf Glover

Publisher: Tavis Leaf Glover

Published: 2019-02-25

Total Pages: 506

ISBN-13: 1733761225

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Serious visual artists can now easily understand and apply the secret geometry that masters used to create remarkable art. Superior mathematical skills aren’t required because there are hundreds of excellent step-by-step diagrams to explain everything with simplicity. Learn how the ancient and modern masters used dynamic symmetry to promote unity, movement, rhythm, and strength. These qualities, along with many others, allowed their art to have visual clarity, impact, and stand the test of time. This is an essential book for painters, photographers, sculptors, and cinematographers that hold composition and design with a high priority. For far too long, artists have been stuck with the basic tools of artistic composition, like the rule of thirds and leading lines. Unfortunately, we’re incapable of reaching the master level if all we know are the basics. Powerful tools like dynamic symmetry and other composition techniques have been kept a secret from all of us. It’s time to learn of them, push past any plateau that stands in our way, and finally unlock our true potential!

Digital Foundations

Author: xtine burrough

Publisher: Peachpit Press

Published: 2008-12-11

Total Pages: 563

ISBN-13: 0132104237

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Fuses design fundamentals and software training into one cohesive book! The only book to teach Bauhaus design principles alongside basic digital tools of Adobe's Creative Suite, including the recently released Adobe CS4 Addresses the growing trend of compressing design fundamentals and design software into the same course in universities and design trade schools. Lessons are timed to be used in 50-minute class sessions. Digital Foundations uses formal exercises of the Bauhaus to teach the Adobe Creative Suite. All students of digital design and production—whether learning in a classroom or on their own—need to understand the basic principles of design in order to implement them using current software. Far too often design is left out of books that teach software. Consequently, the design software training exercise is often a lost opportunity for visual learning. Digital Foundations reinvigorates software training by integrating Bauhaus design exercises into tutorials fusing design fundamentals and core Adobe Creative Suite methodologies. The result is a cohesive learning experience. Design topics and principles include: Composition; Symmetry and Asymmetry; Gestalt; Appropriation; The Bauhaus Basic Course Approach; Color Theory; The Grid; Scale, Hierarchy and Collage; Tonal Range; Elements of Motion. Digital Foundations is an AIGA Design Press book, published under Peachpit's New Riders imprint in partnership with AIGA, the professional association for design.

Mirror Symmetry

Author: Claire Voisin

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 148

ISBN-13: 9780821819470

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This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the Calabi-Yau case. The book concludes with the first "naive" Givental computation, which is a mysterious mathematical justification of the computation of Candelas, et al.

Symmetry Comes of Age

Author: Dorothy Koster Washburn

Publisher: University of Washington Press

Published: 2004

Total Pages: 396

ISBN-13: 9780295983660

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The two volumes together offer readers a new window into the communicative importance of design."--Jacket.

Canon of Design

Author: Tavis Leaf Glover

Publisher: Tavis Leaf Glover

Published: 2014-12-22

Total Pages: 127

ISBN-13: 1320107699

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There’s nothing more important to the future of your artwork than to educate and nurture the unique talent you were born to share with the world. The Canon of Design represents artistic integrity, and enables you to leave your mark on this earth as one of the most talented visual communicators ever known. Learn the language of design to stand with the great masters and reflect the beauty prominently found in nature. This field manual is written to you, for you, and will help shorten your journey to achieving artistic excellence!

Dynamical Symmetry

Author: Carl Wulfman

Publisher: World Scientific

Published: 2011

Total Pages: 459

ISBN-13: 9814291366

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Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.

Fearful Symmetry

Author: A. Zee

Publisher: Princeton University Press

Published: 2015-10-01

Total Pages: 376

ISBN-13: 1400874505

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An engaging exploration of beauty in physics, with a foreword by Nobel Prize–winning physicist Roger Penrose The concept of symmetry has widespread manifestations and many diverse applications—from architecture to mathematics to science. Yet, as twentieth-century physics has revealed, symmetry has a special, central role in nature, one that is occasionally and enigmatically violated. Fearful Symmetry brings the incredible discoveries of the juxtaposition of symmetry and asymmetry in contemporary physics within everyone's grasp. A. Zee, a distinguished physicist and skillful expositor, tells the exciting story of how contemporary theoretical physicists are following Einstein in their search for the beauty and simplicity of Nature. Animated by a sense of reverence and whimsy, Fearful Symmetry describes the majestic sweep and accomplishments of twentieth-century physics—one of the greatest chapters in the intellectual history of humankind.

Symmetry

Author: István Hargittai

Publisher: Elsevier

Published: 2014-05-23

Total Pages: 1068

ISBN-13: 1483149528

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International Series in Modern Applied Mathematics and Computer Science, Volume 10: Symmetry: Unifying Human Understanding provides a tremendous scope of “symmetry , covering subjects from fractals through court dances to crystallography and literature. This book discusses the limits of perfection, symmetry as an aesthetic factor, extension of the Neumann-Minnigerode-Curie principle, and symmetry of point imperfections in solids. The symmetry rules for chemical reactions, matching and symmetry of graphs, mosaic patterns of H. J. Woods, and bilateral symmetry in insects are also elaborated. This text likewise covers the crystallographic patterns, Milton's mathematical symbol of theodicy, symmetries of soap films, and gapon formalism. This volume is a good source for researchers and specialists concerned with symmetry.