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Author: Frank A. Farris
Publisher: Princeton University Press
ISBN: 0691161739
Category : Art
Languages : en
Pages : 246
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Book Description
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.
Author: Frank A. Farris
Publisher: Princeton University Press
ISBN: 0691161739
Category : Art
Languages : en
Pages : 246
Get Book Here
Book Description
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.
Author: Frank A. Farris
Publisher: Princeton University Press
ISBN: 1400865670
Category : Art
Languages : en
Pages : 247
Get Book Here
Book Description
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.
Author: Jay Hambidge
Publisher:
ISBN:
Category : Decoration and ornament
Languages : en
Pages : 216
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Book Description
Author: xtine burrough
Publisher: Peachpit Press
ISBN: 0132104237
Category :
Languages : en
Pages : 563
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Book Description
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.
Author: Kentaro Hori
Publisher: American Mathematical Soc.
ISBN: 0821829556
Category : Mathematics
Languages : en
Pages : 954
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Book Description
This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
Author: Nikita Prokhorov
Publisher: New Riders
ISBN: 0133086461
Category : Computers
Languages : en
Pages : 363
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Book Description
Typography, when coupled with unbridled creativity, craftsmanship, and obsession, can take the mesmerizing form of an ambigram. Ambigrams are typographic designs that combine optical illusion, symmetry, and visual perception. The resulting word or phrase can be read in any number of orientations, viewpoints, or directions. Here is your master class in the art and craft of the ambigram! Curated by graphic and ambigram designer Nikita Prokhorov, this book offers a thorough introduction to the esoteric artistic movement made popular by Dan Brown’s novel Angels & Demons. You’ll find insightful introductions to the ambigram from an allstar panel of design judges, including Scott Kim, John Langdon, Maggie Macnab, Cheryl Savala, Jessica Hische, Stefan G. Bucher, and Scot Morris. Next comes a series of case studies that includes sketches and the thought process behind the creation of some fascinating ambigrams. Finally, the showcase section presents numerous curated artworks from ambigramists around the world. Equipped with the expert techniques and inspiring examples found in these pages, you’ll be ready to start creating your own ambigrams! Stunning showcase of ambigram artwork from around the world Insightful commentary from an all-star panel of ambigram luminaries In-depth case studies illustrating the creation of ambigrams from start to finish
Author: Claire Voisin
Publisher: American Mathematical Soc.
ISBN: 9780821819470
Category : Mathematics
Languages : en
Pages : 148
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Book Description
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.
Author: Sandra L. Atkins
Publisher: Routledge
ISBN: 1000461173
Category : Education
Languages : en
Pages : 187
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Book Description
What meanings do your students have for key mathematics concepts? What meanings do you wish them to have? Creating a Language-Rich Math Class offers practical approaches for developing conceptual understandings by connecting concrete, pictorial, verbal, and symbolic representations. The focus is on making mathematics memorable instead of on memorizing. You’ll learn strategies for introducing students to math language that gives meaning to the terms and symbols they use every day; for building flexibility and precision in students’ use of math language; and for structuring activities to make them more language-rich. This second edition also provides strategies for helping students to at times be quiet and listen to their peers; for purposefully using language to introduce students to more complex mathematical symbolism and algebraic properties; and for using writing prompts to zoom in on the meanings that individual students have given to the language-rich experiences. Appropriate for elementary teachers and instructional coaches, the book also includes features such as Investigations to Try and Questions for Reflection to help you incorporate these ideas into your practice. In addition, there are Blackline masters of game cards and puzzles, which can also be found on our website for free download at http://www.routledge.com/9780367759957.
Author: HowExpert
Publisher: HowExpert
ISBN:
Category : Crafts & Hobbies
Languages : en
Pages : 160
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Book Description
If you're ready to master the art of rock balancing, find inner peace, and connect with nature, HowExpert Guide to Rock Balancing is the ideal resource for you. This comprehensive guide covers everything from the basics of stone stacking to creating meaningful cairns that stand the test of time. Whether you’re a beginner or a seasoned balancer, this book will help elevate your skills and deepen your connection to the meditative practice of rock balancing. Introduction - Learn the fundamentals of stone stacking, how to find balance in nature, and the spiritual and environmental importance of rock balancing. Part 1: Perfecting Stone Stacking - Chapter 1: The Basics of Stone Stacking – Master balance, gravity, and choosing the right stones for stable stacks. - Chapter 2: Advanced Stone Stacking Techniques – Refine your skills with precision techniques, layering, and overcoming common challenges. - Chapter 3: Integrating Creativity into Stone Stacking – Balance colors, textures, and incorporate unique materials to express your creativity. Part 2: Achieving Balanced Stones - Chapter 4: The Art of Balance – Cultivate mindfulness as you experiment with both symmetrical and asymmetrical formations. - Chapter 5: Tools and Techniques for Stability – Use natural elements and advanced methods to stabilize larger stones with ease. - Chapter 6: The Physics of Rock Balancing – Understand the science behind weight distribution, friction, and engineering principles to improve your balancing. Part 3: Creating Cairns - Chapter 7: The Cultural Significance of Cairns – Explore the historical roles of cairns as trail markers, ritual symbols, and their modern environmental impact. - Chapter 8: Building and Preserving Cairns – Learn how to build durable cairns while balancing artistic expression with ethical considerations. - Chapter 9: Rock Balancing as a Cultural Dialogue – Engage with rock balancing as a universal language and a way to share stories through stones. Part 4: The Mindful Practice of Rock Balancing - Chapter 10: Rock Balancing as Meditation – Integrate rock balancing into your daily routine as a meditative practice, both solo and in groups. - Chapter 11: Connecting with Nature Through Rock Balancing – Practice eco-friendly techniques, choose meaningful locations, and document your work. - Chapter 12: The Therapeutic Benefits of Rock Balancing – Discover the mental health benefits, including stress relief and clarity, and how rock balancing can be used therapeutically. Part 5: The Future of Rock Balancing - Chapter 13: Trends and Innovations in Rock Balancing – Stay current with trends, from competitions to technological advancements and environmental activism. - Chapter 14: Rock Balancing Resources – Access valuable resources such as books, guides, and workshops to continue developing your practice. - Chapter 15: The Legacy of Rock Balancing – Reflect on the influence of rock balancing in modern art and inspire future generations to carry on this ancient practice. Conclusion - Reflect on the deep connection between balance in rock stacking and life, and join the global community dedicated to this timeless practice. Appendices - Explore a glossary of terms, recommended tools, additional resources, and notable rock balancing sites worldwide. Take your rock balancing skills to the next level with HowExpert Guide to Rock Balancing. Whether you pursue it for mindfulness, creativity, or artistic expression, this guide provides all the tools you need. Start your journey today and experience the peace, balance, and creativity that rock balancing brings to life. Grab your copy now and begin mastering the art of stone stacking! HowExpert publishes how to guides on all topics from A to Z.
Author: David W. Farmer
Publisher: American Mathematical Soc.
ISBN: 0821804502
Category : Mathematics
Languages : en
Pages : 112
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Book Description
Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.
