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Author: Frank A. Farris
Publisher: Princeton University Press
ISBN: 1400865670
Category : Art
Languages : en
Pages : 247
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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: 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: George E. Martin
Publisher: Springer Science & Business Media
ISBN: 1461256801
Category : Mathematics
Languages : en
Pages : 251
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Book Description
Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. The detailed development of the isometries of the plane is based on only the most elementary geometry and is appropriate for graduate courses for secondary teachers.
Author: James T. Smith
Publisher: John Wiley & Sons
ISBN: 1118031032
Category : Mathematics
Languages : en
Pages : 486
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Book Description
A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: Ample exercises designed to promote effective problem-solvingstrategies Insight into novel uses of Euclidean geometry More than 300 figures accompanying definitions and proofs A comprehensive and annotated bibliography Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.
Author: Goulnara N. Arzhantseva
Publisher: Springer Science & Business Media
ISBN: 3764384123
Category : Mathematics
Languages : en
Pages : 256
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Book Description
This volume has its origins in the Barcelona Conference in Group Theory (July 2005) and the conference "Asymptotic and Probabilistic Methods in Geometric Group Theory" held in Geneva (June 2005). Twelve peer-reviewed research articles written by experts in the field present the most recent results in abstract and geometric group theory. In particular there are two articles by A. Juhász.
Author: Jost-Hinrich Eschenburg
Publisher: Springer Nature
ISBN: 3658386401
Category : Mathematics
Languages : en
Pages : 168
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Book Description
This book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified. The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry. The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions. This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Author: Norman W. Johnson
Publisher: Cambridge University Press
ISBN: 1107103401
Category : Mathematics
Languages : en
Pages : 455
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Book Description
A readable exposition of how Euclidean and other geometries can be distinguished using linear algebra and transformation groups.
Author: W. W. Sawyer
Publisher: Courier Corporation
ISBN: 0486152774
Category : Mathematics
Languages : en
Pages : 228
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Book Description
This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.
Author: Jay Friedenberg
Publisher: Lulu.com
ISBN: 1304491153
Category : Art
Languages : en
Pages : 119
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Book Description
Geometric wallpaper patterns for use in a wide variety of applications. Basic geometric shapes are modified and repeated to create intricate designs for use in web, graphic design and crafts. Ninety-six different patterns are presented in attractive color schemes. Perfect for surface pattern design. Use to create fabrics, quilts, ornament and more.
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: E. H. Lockwood
Publisher: CUP Archive
ISBN: 9780521216852
Category : Mathematics
Languages : en
Pages : 248
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Book Description
Symmetry is of interest in two ways, artistic and mathematical. It underlies much scientific thought, playing an important role in chemistry and atomic physics, and a dominant one in crystallography. It is important in architectural and engineering design and particularly in the decorative arts. This book provides a comprehensive account of symmetry in a form acceptable to readers without much detailed mathematical knowledge or experience who nevertheless want to understand the basic principles of the subject. It will be useful in school and other libraries and as preliminary reading for students of crystallography. The treatment is geometrical, which should appeal to art students and to readers whose mathematical interests are that way inclined.
