Polyominoes: A Guide to Puzzles and Problems in Tiling PDF Download
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Author: George E. Martin
Publisher: American Mathematical Soc.
ISBN: 1470457342
Category : Mathematics
Languages : en
Pages : 199
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Book Description
Polyominoes will delight not only students and teachers of mathematics at all levels, but will be appreciated by anyone who likes a good geometric challenge. There are no prerequisites. If you like jigsaw puzzles, or if you hate jigsaw puzzles but have ever wondered about the pattern of some floor tiling, there is much here to interest you. A polyomino is a shape cut along the lines from square graph paper; the pronunciation of polyomino begins as does polygon and ends as does domino. Tilings, also called tessellations of mosaic patterns, are older than civilization itself. Tiling with polyominoes provides challenges that range from the popular jigsaw-like puzzles to easily understood mathematical research problems. You will find unsolved puzzles and problems of both kinds here. Answers are provided for most of the problems that have known solutions. It is only fair to repeat here the warning stated in the preface to this book, "Playing with polyominoes can be habit forming."
Author: George E. Martin
Publisher: American Mathematical Soc.
ISBN: 1470457342
Category : Mathematics
Languages : en
Pages : 199
Get Book Here
Book Description
Polyominoes will delight not only students and teachers of mathematics at all levels, but will be appreciated by anyone who likes a good geometric challenge. There are no prerequisites. If you like jigsaw puzzles, or if you hate jigsaw puzzles but have ever wondered about the pattern of some floor tiling, there is much here to interest you. A polyomino is a shape cut along the lines from square graph paper; the pronunciation of polyomino begins as does polygon and ends as does domino. Tilings, also called tessellations of mosaic patterns, are older than civilization itself. Tiling with polyominoes provides challenges that range from the popular jigsaw-like puzzles to easily understood mathematical research problems. You will find unsolved puzzles and problems of both kinds here. Answers are provided for most of the problems that have known solutions. It is only fair to repeat here the warning stated in the preface to this book, "Playing with polyominoes can be habit forming."
Author: Solomon W. Golomb
Publisher: Princeton University Press
ISBN: 0691215057
Category : Mathematics
Languages : en
Pages : 204
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Book Description
Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino. Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes.
Author: George Martin
Publisher: Cambridge University Press
ISBN: 9780883855010
Category : Mathematics
Languages : en
Pages : 200
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Book Description
A book for anyone who likes a good geometric challenge.
Author: A. J. Guttmann
Publisher: Springer Science & Business Media
ISBN: 1402099266
Category : Science
Languages : en
Pages : 500
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Book Description
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.
Author: Alan Schoen
Publisher: CRC Press
ISBN: 1439865000
Category : Mathematics
Languages : en
Pages : 320
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Book Description
The tradition of honoring Martin Gardner continues with this edited collection of articles by those who have been inspired by Gardner to enter mathematics, to enter magic, to bring magic into their mathematics, or to bring mathematics into their magic. Contributing authors include world-leading puzzle designers, puzzle collectors, mathematicians, a
Author: Michele D’Adderio
Publisher: American Mathematical Society
ISBN: 1470471574
Category : Mathematics
Languages : en
Pages : 138
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Book Description
View the abstract.
Author: Mizuho Hoshi
Publisher: Springer
ISBN: 3319986546
Category : Computers
Languages : en
Pages : 581
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Book Description
This book constitutes the proceedings of the 22nd International Conference on Developments in Language Theory, DLT 2018, held in Tokyo, Japan, in September 2018. The 39 full papers presented in this volume were carefully reviewed and selected from 84 submissions. The papers cover the following topics and areas: combinatorial and algebraic properties of words and languages; grammars, acceptors and transducers for strings, trees, graphics, arrays; algebraic theories for automata and languages; codes; efficient text algorithms; symbolic dynamics; decision problems; relationships to complexity theory and logic; picture description and analysis, polyominoes and bidimensional patterns; cryptography; concurrency; celluar automata; bio-inspired computing; quantum computing.
Author: Adrian Horia Dediu
Publisher: Springer
ISBN: 3642009824
Category : Mathematics
Languages : en
Pages : 766
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Book Description
This book constitutes the refereed proceedings of the Third International Conference on Language and Automata Theory and Applications, LATA 2009, held in Tarragona, Spain, in April 2009. The 58 revised full papers presented together with 3 invited lectures and two tutorials were carefully reviewed and selected from 121 submissions. The papers address all the various issues related to automata theory and formal languages.
Author: Reneta P. Barneva
Publisher: Springer
ISBN: 3319071483
Category : Computers
Languages : en
Pages : 284
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Book Description
This volume constitutes the refereed proceedings of the 16th International Workshop on Combinatorial Image Analysis, IWCIA 2014, held in Brno, Czech Republic, in May 2014. The 20 revised full papers and 3 invited papers presented were carefully reviewed and selected from numerous submissions. The topics covered include discrete geometry and topology in imaging science, new results in image representation, segmentation, grouping, and reconstruction, medical image processing.
Author: Peter W. Hawkes
Publisher: Elsevier
ISBN: 0080490093
Category : Technology & Engineering
Languages : en
Pages : 263
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Book Description
The subjects reviewed in the Advances in Imaging and Electron Physics series cover a broad range of themes including microscopy, electromagnetic fields and image coding. This book is essential reading for electrical engineers, applied mathematicians and robotics experts. - Emphasizes broad and in depth article collaborations between world-renowned scientists in the field of image and electron physics - Presents theory and it's application in a practical sense, providing long awaited solutions and new findings - Bridges the gap between academic researchers and R&D designers by addressing and solving daily issues
