tilings and patterns dover books on mathematics

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Tilings And Patterns

Author : Branko Grünbaum
ISBN : 0486469816
Genre : Mathematics
File Size : 20. 53 MB
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This definitive book on tiling includes 520 figures and over 100 tables. Accessible to anyone with a grasp of geometry, its illustrated examples feature related problems and references. 1987 edition.

Tilings And Patterns

Author : Branko Grünbaum
ISBN : 0716719983
Genre : Mathematics
File Size : 76. 97 MB
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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.

Mosaic And Tessellated Patterns

Author : John Willson
ISBN : 9780486136332
Genre : Art
File Size : 33. 69 MB
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An expert "op art" designer explains what tessellated patterns are and how they are formed, relates the history of tessellated designs from their beginnings in Rome. 179 line drawings. 32 full-page plates.

Introductory Tiling Theory For Computer Graphics

Author : Craig S. Kaplan
ISBN : 9781608450176
Genre : Computers
File Size : 86. 82 MB
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Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science. This synthesis lecture introduces the mathematical and algorithmic foundations of tiling theory to a computer graphics audience. The goal is primarily to introduce concepts and terminology, clear up common misconceptions, and state and apply important results. The book also describes some of the algorithms and data structures that allow several aspects of tiling theory to be used in practice. Table of Contents: Introduction / Tiling Basics / Symmetry / Tilings by Polygons / Isohedral Tilings / Nonperiodic and Aperiodic Tilings / Survey

Linear Geometry

Author : Rafael Artzy
ISBN : 0486466272
Genre : Mathematics
File Size : 68. 85 MB
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Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transformations and their groups in the Euclidean plane, explaining algebraic concepts as they arise. A brief account of Poincaré's model of the hyperbolic plane and its transformation group follow. Succeeding chapters contain a systematic treatment of affine, Euclidean, and projective spaces over fields that emphasizes transformations and their groups, along with an outline of results involving other geometries. An examination of the foundations of geometry starts from rudimentary projective incidence planes, then gradually adjoins axioms and develops various non-Desarguesian, Desarguesian, and Pappian planes, their corresponding algebraic structures, and their collineation groups. The axioms of order, continuity, and congruence make their appearance and lead to Euclidean and non-Euclidean planes. Lists of books for suggested further reading follow the third and fourth chapters, and the Appendix provides lists of notations, axioms, and transformation groups.

Configurations Of Points And Lines

Author : Branko Grünbaum
ISBN : 9780821843086
Genre : Mathematics
File Size : 68. 39 MB
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This is the only book on the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines since its beginning in 1876. It covers all the advances in the field since the revival of interest in geometric configurations some 20 years ago. The author's contributions are central to this revival. In particular, he initiated the study of 4-configurations (that is, those that contain four points on each line, and four lines through each point); the results are fully described in the text. The main novelty in the approach to all geometric configurations is the concentration on their symmetries, which make it possible to deal with configurations of rather large sizes. The book brings the readers to the limits of present knowledge in a leisurely way, enabling them to enjoy the material as well as entice them to try their hand at expanding it.

Designing Tessellations

Author : Jinny Beyer
ISBN : UCSD:31822027918796
Genre : Crafts & Hobbies
File Size : 61. 19 MB
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Jinny Beyer deftly interweaves inspiration and technique to create a guide to tessellations, amazing motifs, that interlock perfectly to flow across a surface. Learn the mystery of how complex designs are achieved and how thousands of patterns are possible by manipulating the simplest of shapes.

Introduction To Tessellations

Author : Dale Seymour
ISBN : 0866514619
Genre : Mathematics
File Size : 89. 78 MB
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Presents an introduction to tessellations and geometric design, including polygons, Islamic art designs, Escher-type tessellations, and tessellating letters, along with step-by-step instructions for creating tessellations.

Spherical Models

Author : Magnus J. Wenninger
ISBN : 9780486143651
Genre : Mathematics
File Size : 43. 20 MB
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Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just a ruler and compass. 1979 edition.

Penrose Tiles To Trapdoor Ciphers

Author : Martin Gardner
ISBN : 0883855216
Genre : Mathematics
File Size : 21. 50 MB
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Here is another collection drawn from Martin Gardner's 'Mathematical Games' column in Scientific American. Each chapter explores a different theme, for example fractals, surreal numbers, the sculptures of Berrocal, tiling the plane, Ramsey theory and code breaking, all combining to create a rich diet of recreational mathematics. Most chapters can be readily understood by the uninitiated: at each turn there are challenges for the reader and a wealth of references for further reading. Gardner's clarity of style and ability systematically to simplify the complex make this an excellent vehicle in which to start or continue an interest in recreational mathematics.

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