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| Author | : Sherman Stein |
| Publisher | : Cambridge University Press |
| Total Pages | : 236 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9780883850282 |
A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
| Author | : Charles Radin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 134 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 082181933X |
"Miles of Tiles" is a mathematics lesson for middle school classes requiring students to calculate the number and cost of tiles needed to cover the floor of the classroom. This lesson includes Internet activities. "Miles of Tiles" is presented as a service of the Link-to-Learn Professional Development Project of Pennsylvania, a state-sponsored educational technology initiative.
| Author | : Lorenzo Adlai Sadun |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 131 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821847279 |
"This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.
| Author | : Sherman K. Stein |
| Publisher | : Mathematical Association of America (MAA) |
| Total Pages | : 222 |
| Release | : 2014-05-10 |
| Genre | : MATHEMATICS |
| ISBN | : 9781614440246 |
A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
| Author | : Sherman K. Stein |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1994 |
| Genre | : Algebra |
| ISBN | : 9780883850008 |
There is a long tradition of geometric questions requiring algebra for their answers. The oldest go back to the Greeks, such as "Can we construct a square with the same area as that of a given disk?" many of which were not resolved until mathematicians concluded that [lowercase Greek]Pi is transcendental. There are many questions that appear to focus on geometry, but which require algebra to solve. This book looks at the algebra used to solve tiling and related problems. One purpose of the text is to bring abstract algebra ideas down to earth by applying them in geometric settings. The text is intended for undergraduate and graduate students with at least a semester of algebra, and experienced mathematicians. For both beginners and experts, there are questions that have not yet been answered, which have been labeled "Problems" to distinguish them from the exercises.
| Author | : Sherman K. Stein |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 207 |
| Release | : 1993-12-31 |
| Genre | : |
| ISBN | : 1470451115 |
Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers, and professional mathematicians will find the book equally appealing. Beginners will find the exercises and the appendices especially useful. The unsolved problems will challenge both beginners and experts. The book could serve as the basis of an undergraduate or graduate seminar or a source of applications to enrich an algebra or geometry course.
| Author | : Colin Adams |
| Publisher | : American Mathematical Society |
| Total Pages | : 310 |
| Release | : 2023-08-28 |
| Genre | : Mathematics |
| ISBN | : 1470474611 |
Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.
| Author | : Colin Adams |
| Publisher | : American Mathematical Society |
| Total Pages | : 310 |
| Release | : 2022-08-18 |
| Genre | : Mathematics |
| ISBN | : 1470468972 |
Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there is both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.
| Author | : Craig S. Kaplan |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 103 |
| Release | : 2009 |
| Genre | : Computers |
| ISBN | : 1608450171 |
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
| Author | : Francesco D'Andrea |
| Publisher | : Springer Nature |
| Total Pages | : 203 |
| Release | : 2023-08-19 |
| Genre | : Mathematics |
| ISBN | : 3031284283 |
This book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the '70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most famous example, started as recreational mathematics and soon attracted the interest of scientists for their possible application in the description of quasi-crystals. The purpose of this survey, illustrated with more than 200 figures, is to introduce the curious reader to this beautiful topic and be a reference for some proofs that are not easy to find in the literature. The volume covers many aspects of Penrose tilings, including the study, from the point of view of Connes' Noncommutative Geometry, of the space parameterizing these tilings.
