creating symmetry the artful mathematics of wallpaper patterns

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Creating Symmetry

Author : Frank A. Farris
ISBN : 9781400865673
Genre : Art
File Size : 82. 14 MB
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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.

Creating Symmetry

Author : Frank A. Farris
ISBN : 0691161739
Genre : Art
File Size : 46. 65 MB
Format : PDF, ePub, Mobi
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"Frank's rich artistry vibrantly enlivens the mathematics of symmetry. What a treat for the eye and the mind!"--Michael Starbird, The University of Texas at Austin "The imagery in this book is attractive and engaging, and illustrates Farris's excellent command of the mathematical techniques and his strong sense of visual design. General readers will appreciate the beauty of the images and will find incentive to learn how mathematics can be used in creative ways to produce art."--George W. Hart, coauthor of "Zome Geometry: Hands-on Learning with Zome Models" "This unique book takes an entirely new approach to creating images with symmetry. The pictures are compelling and Farris presents the material in an inviting manner. He leads readers into interesting areas of mathematics not usually encountered in undergraduate courses, and rarely, if ever, encountered as a way to study symmetry."--Doris Schattschneider, author of "M. C. Escher: Visions of Symmetry" "In "Creating Symmetry," Farris explores the concept of symmetry and its application to creating artistic patterns in two dimensions. The result is a set of algorithmic tools for transforming ordinary photographs into rosettes and wavelike murals decorated with colorful swirls and gradients. It is difficult to imagine a more engaging focus for teaching the mathematics of symmetry."--Kenneth Libbrecht, author of "The Secret Life of a Snowflake: An Up-Close Look at the Art and Science of Snowflakes" ""Creating Symmetry" is a stunning fusion of mathematics and art, applying the mathematics of symmetry to create beautiful patterns. But the beauty runs far deeper: the mathematical insights involved are supremely beautiful in their own right. If you want to know why there are exactly 17 basic types of wallpaper, what their structure is, and which other mathematical ideas are related, or if you just want to see some amazing pictures, look no further."--Ian Stewart, author of "Professor Stewart s Casebook of Mathematical Mysteries" ""Creating Symmetry" is a remarkable, one-of-a-kind book, with unique and beautiful pictures. While plane symmetry groups have been the subject of other books, Farris s approach is fresh and accessible."--John Stillwell, author of "Roads to Infinity: The Mathematics of Truth and Proof" "Farris has written an amazing book. His vision is expansive, his enthusiasm is contagious, and the illustrations are intriguing and beautiful. Farris enables readers to gain a deep appreciation and understanding of the mathematics behind symmetry and his novel approach to creating symmetrical patterns. No other book comes close."--Thomas Q. Sibley, author of "Foundations of Mathematics" "This book introduces readers to the fascinating interplay of geometry, complex function theory, abstract algebra, complex domain coloring, Fourier series, and aesthetics in producing really beautiful images. Farris shows how structured forms of symmetry can be constructed in a disciplined way from first mathematical principles, and how artistically pleasing images can communicate sophisticated but understandable mathematics."--Paul Zorn, author of "Understanding Real Analysis""

Beautiful Geometry

Author : Eli Maor
ISBN : 9781400848331
Genre : Mathematics
File Size : 49. 32 MB
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If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.

Creating Symmetry The Artful Mathematics Of Wallpaper Patterns By Frank A Farris

Author :
ISBN : OCLC:1032080038
Genre :
File Size : 29. 45 MB
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Tilings And Patterns

Author : Branko Grünbaum
ISBN : 0716719983
Genre : Mathematics
File Size : 86. 2 MB
Format : PDF
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Tilings and Patterns: An Introduction presents in convenient paperback form the first half of Tilings and Patterns. Omitting the more specialized material of the earlier volume, this abbreviated edition make's the authors' contributions to tiling theory and its practical applications accessible to a wide audience.

Mathematics In Nature

Author : John A. Adam
ISBN : 9781400841011
Genre : Mathematics
File Size : 69. 46 MB
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From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

Symmetry In Chaos

Author : Michael Field
ISBN : 0898717701
Genre : Chaotic behavior in systems
File Size : 59. 89 MB
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Symmetry suggests order and regularity whilst chaos suggests disorder and randomness. 'Symmetry in Chaos' is an exploration of how combining seemingly contradictory principles can lead to the construction of striking and beautiful images. This book is an engaging look at the interplay of art and mathematics.


Author : Kristopher Tapp
ISBN : 1461402999
Genre : Mathematics
File Size : 21. 97 MB
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This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.

Mathematics And Art

Author : Claude Bruter
ISBN : 9783662049099
Genre : Mathematics
File Size : 73. 61 MB
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Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.

Pattern Design

Author : Lewis Foreman Day
ISBN : UOM:39015009096192
Genre : Decoration and ornament
File Size : 40. 94 MB
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Master techniques for using pattern in wide range of design applications including architectural, textiles, print, more. Wealth of technical information. Over 270 design illustrations.

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