# Search Results for "tilings-and-patterns-dover-books-on-mathematics"

## Introductory Tiling Theory for Computer Graphics

**Author**: Craig Kaplan**Publisher:**Morgan & Claypool Publishers**ISBN:**160845018X**Category:**Computers**Page:**113**View:**7400

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

## Shapes, Space, and Symmetry

**Author**: Alan Holden**Publisher:**Courier Corporation**ISBN:**9780486268514**Category:**Mathematics**Page:**200**View:**1266

Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.

## Groups and Symmetry

*A Guide to Discovering Mathematics*

**Author**: David W. Farmer**Publisher:**American Mathematical Soc.**ISBN:**0821804502**Category:**Mathematics**Page:**102**View:**2171

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.

## Introduction to Tessellations

**Author**: Dale Seymour,Jill Britton**Publisher:**Dale Seymour Publication**ISBN:**9780866514613**Category:**Mathematics**Page:**256**View:**7144

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**Publisher:**Courier Corporation**ISBN:**0486143651**Category:**Mathematics**Page:**176**View:**8468

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.

## Journey through Mathematics

*Creative Episodes in Its History*

**Author**: Enrique A. González-Velasco**Publisher:**Springer Science & Business Media**ISBN:**0387921540**Category:**Mathematics**Page:**466**View:**2911

This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation. The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.

## Polyhedra

*A Visual Approach*

**Author**: Anthony Pugh**Publisher:**Univ of California Press**ISBN:**9780520030565**Category:**Dômes géodésiques**Page:**118**View:**2985

## Mosaic and Tessellated Patterns

*How to Create Them, with 32 Plates to Color*

**Author**: John Willson**Publisher:**Courier Corporation**ISBN:**0486136337**Category:**Art**Page:**64**View:**3040

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.

## Twists, Tilings, and Tessellations

*Mathematical Methods for Geometric Origami*

**Author**: Robert J. Lang**Publisher:**CRC Press**ISBN:**148226241X**Category:**Mathematics**Page:**756**View:**4101

Twists, Tilings, and Tessellation describes the underlying principles and mathematics of the broad and exciting field of abstract and mathematical origami, most notably the field of origami tessellations. It contains folding instructions, underlying principles, mathematical concepts, and many beautiful photos of the latest work in this fast-expanding field.

## Miles of Tiles

**Author**: Charles Radin**Publisher:**American Mathematical Soc.**ISBN:**082181933X**Category:**Mathematics**Page:**120**View:**5659

``In this book, we try to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics--mathematics unforeseen from the motivating problem ... '' --from the Preface The common thread throughout this book is aperiodic tilings; the best-known example is the ``kite and dart'' tiling. This tiling has been widely discussed, particularly since 1984 when it was adopted to model quasicrystals. The presentation uses many different areas of mathematics and physics to analyze the new features of such tilings. Although many people are aware of the existence of aperiodic tilings, and maybe even their origin in a question in logic, not everyone is familiar with their subtleties and the underlying rich mathematical theory. For the interested reader, this book fills that gap. Understanding this new type of tiling requires an unusual variety of specialties, including ergodic theory, functional analysis, group theory and ring theory from mathematics, and statistical mechanics and wave diffraction from physics. This interdisciplinary approach also leads to new mathematics seemingly unrelated to the tilings. Included are many worked examples and a large number of figures. The book's multidisciplinary approach and extensive use of illustrations make it useful for a broad mathematical audience.

## Creating Symmetry

*The Artful Mathematics of Wallpaper Patterns*

**Author**: Frank A. Farris**Publisher:**Princeton University Press**ISBN:**1400865670**Category:**Art**Page:**248**View:**1091

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.

## Regular Polytopes

**Author**: H. S. M. Coxeter**Publisher:**Courier Corporation**ISBN:**0486141586**Category:**Mathematics**Page:**368**View:**444

Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.

## The Symmetries of Things

**Author**: John H. Conway,Heidi Burgiel,Chaim Goodman-Strauss**Publisher:**CRC Press**ISBN:**1439864896**Category:**Mathematics**Page:**448**View:**8528

Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

## Chaotic Dynamics

*Fractals, Tilings, and Substitutions*

**Author**: Geoffrey R. Goodson**Publisher:**Cambridge University Press**ISBN:**1107112672**Category:**Mathematics**Page:**350**View:**2767

This rigorous undergraduate introduction to dynamical systems is an accessible guide for mathematics students advancing from calculus.

## Handbook of Regular Patterns

*An Introduction to Symmetry in Two Dimensions*

**Author**: Peter S. Stevens**Publisher:**MIT Press (MA)**ISBN:**9780262690881**Category:**Design**Page:**400**View:**5276

Examines the structural anatomy of patterns, shows how reflections, rotations, and translations create symmetrical patterns, and shows examples from textiles, pottery, mosaics, natural forms, and Escher prints

## Treks into Intuitive Geometry

*The World of Polygons and Polyhedra*

**Author**: Jin Akiyama,Kiyoko Matsunaga**Publisher:**Springer**ISBN:**4431558438**Category:**Mathematics**Page:**425**View:**1955

This book is written in a style that uncovers the mathematical theories buried in our everyday lives such as examples from patterns that appear in nature, art, and traditional crafts, and in mathematical mechanisms in techniques used by architects. The authors believe that through dialogues between students and mathematicians, readers may discover the processes by which the founders of the theories came to their various conclusions―their trials, errors, tribulations, and triumphs. The goal is for readers to refine their mathematical sense of how to find good questions and how to grapple with these problems. Another aim is to provide enjoyment in the process of applying mathematical rules to beautiful art and design by examples that highlight the wonders and mysteries from our daily lives. To fulfill these aims, this book deals with the latest unique and beautiful results in polygons and polyhedra and the dynamism of geometrical research history that can be found around us. The term "intuitive geometry" was coined by Lászlo Fejes Tóth to refer to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book allows people to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity.

## Polyominoes

*Puzzles, Patterns, Problems, and Packings*

**Author**: Solomon W. Golomb**Publisher:**Princeton University Press**ISBN:**9780691024448**Category:**Mathematics**Page:**184**View:**2173

For professional mathematicians and amateurs seeking further challenge, the author offers a host of new problems that remain to be solved.