Polyominoes: puzzles, patterns, problems, and packings
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? If you have a set of pentominoes (shapes consisting of five squares) could you cover a rectangle with them? What would...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
1994
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006584309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Zusammenfassung: | 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? If you have a set of pentominoes (shapes consisting of five squares) could you cover a rectangle with them? What would happen if you had cubes instead of squares? Could you pack a box with them Posing problems and giving answers along the way, Golomb invites the reader to play with these mathematical structures and develop on understanding of their extraordinary properties. In this new edition, he addresses, for example, the properties of octominoes and enneominoes and the problem of how to cover a donut 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 |
| Abstract: | Inspiring popular video games like Tetris while contributing to the study of combinotorial 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 polyominoes, incorporoting the most important recent developments |
| Umfang: | XII, 184 S. graph. Darst. |
| ISBN: | 0691085730 |
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| 520 | 3 | |a Inspiring popular video games like Tetris while contributing to the study of combinotorial 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 polyominoes, incorporoting the most important recent developments | |
| 520 | |a 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? If you have a set of pentominoes (shapes consisting of five squares) could you cover a rectangle with them? What would happen if you had cubes instead of squares? Could you pack a box with them | ||
| 520 | |a Posing problems and giving answers along the way, Golomb invites the reader to play with these mathematical structures and develop on understanding of their extraordinary properties. In this new edition, he addresses, for example, the properties of octominoes and enneominoes and the problem of how to cover a donut 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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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface to the Revised Edition ix
Preface to the First Edition xi
Chapter 1. Polyominoes and Checkerboards 3
Chapter 2. Patterns and Polyominoes 12
Chapter 3. Where Pentominoes Will Not Fit 20
Chapter 4. Backtracking and Impossible
Constructions 30
Chapter 5. Some Theorems about Counting 43
Chapter 6. Bigger Polyominoes and Higher
Dimensions 70
Chapter 7. Generalizations of Polyominoes 85
Chapter 8. Tiling Rectangles with Polyominoes 97
Chapter 9. Some Truly Remarkable Results 111
Appendix A. Answers to Exercises in Chapter 5 127
Appendix B. Problem Compendium 133
Appendix C. Golomb s Twelve Pentomino
Problems, by Andy Liu 146
Appendix D. Klarner s Konstant and the
Enumeration of N Ominoes 152
Glossary 155
Bibliography for the First Edition 160
Comprehensive Bibliography 162
Name Index 183
|
| any_adam_object | 1 |
| author | Golomb, Solomon W. 1932-2016 |
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| callnumber-raw | QA166.75 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 230 |
| ctrlnum | (OCoLC)29358809 (DE-599)BVBBV009938578 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.6 |
| dewey-search | 511/.6 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV009938578 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:44:50Z |
| institution | BVB |
| isbn | 0691085730 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006584309 |
| oclc_num | 29358809 |
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| owner_facet | DE-12 DE-20 DE-703 DE-29T DE-188 |
| physical | XII, 184 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| spellingShingle | Golomb, Solomon W. 1932-2016 Polyominoes puzzles, patterns, problems, and packings Remplissage et recouvrement (géométrie combinatoire) ram Mathematik Mathematics Polyominoes Polyomino (DE-588)4350416-4 gnd |
| subject_GND | (DE-588)4350416-4 |
| title | Polyominoes puzzles, patterns, problems, and packings |
| title_auth | Polyominoes puzzles, patterns, problems, and packings |
| title_exact_search | Polyominoes puzzles, patterns, problems, and packings |
| title_full | Polyominoes puzzles, patterns, problems, and packings Solomon W. Golomb |
| title_fullStr | Polyominoes puzzles, patterns, problems, and packings Solomon W. Golomb |
| title_full_unstemmed | Polyominoes puzzles, patterns, problems, and packings Solomon W. Golomb |
| title_short | Polyominoes |
| title_sort | polyominoes puzzles patterns problems and packings |
| title_sub | puzzles, patterns, problems, and packings |
| topic | Remplissage et recouvrement (géométrie combinatoire) ram Mathematik Mathematics Polyominoes Polyomino (DE-588)4350416-4 gnd |
| topic_facet | Remplissage et recouvrement (géométrie combinatoire) Mathematik Mathematics Polyominoes Polyomino |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006584309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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