Polyominoes : puzzles, patterns, problems, and packings
著者
書誌事項
Polyominoes : puzzles, patterns, problems, and packings
Princeton University Press, c1994
2nd ed
- : pbk
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注記
Includes bibliographical references (p. [160]-181) and index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780691024448
内容説明
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.
目次
Preface to the Revised EditionPreface to the First EditionCh. 1Polyominoes and Checkerboards3Ch. 2Patterns and Polyominoes12Ch. 3Where Pentominoes Will Not Fit20Ch. 4Backtracking and Impossible Constructions30Ch. 5Some Theorems about Counting43Ch. 6Bigger Polyominoes and Higher Dimensions70Ch. 7Generalizations of Polyominoes85Ch. 8Tiling Rectangles with Polyominoes97Ch. 9Some Truly Remarkable Results111Appendix A. Answers to Exercises in Chapter 5127Appendix B. Problem Compendium133Appendix C. Golomb's Twelve Pentomino Problems146Appendix D. Klamer's Konstant and the Enumeration of N-Ominoes152Glossary155Bibliography for the First Edition160Comprehensive Bibliography162Name Index183
- 巻冊次
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ISBN 9780691085739
内容説明
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 expanded edition, the author takes a new generation of readers on a mathematical journey into the world of polyominoes, incorporating important recent developments. Deceptively simple, polyominoes are a collection of squares joined together along their edges. But how many different polyominoes can you make with 5 squares, 6 squares, n squares? Posing problems and giving answers along the way, Golomb invites the reader to play with these mathematical structures and develop an understanding of their extraordinary properties. In this new edition, he addresses the properties of octominoes and enneominoes and the problem of how to cover a doughnut with polyominoes. An extensive bibliography has been included to guide the reader to other interesting mathematical conundrums and to more advanced mathematical theories of polyominoes.
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