147:
29:
137:
A second
English-language edition of the book was published by the Princeton University Press in 1994. It added to the corrected text of the original addition two more chapters on recent developments, an expanded bibliography, and two appendices, one giving an enumeration of polyominoes and a second
293:
Reviewer
Elizabeth Senger writes that the book has a wide audience of "mathematicians, teachers, students, and puzzle people", and is "well written and easy to read", accessible even to high school level mathematics students. Similarly, Elaine Hale writes that it should be read by "all professional
203:
for counting polyominoes and their packings. Although reviewer M. H. Greenblatt considers this more theoretical material a digression from the main topic of the book, and the book itself suggests that less mathematically-inclined readers skip this material, Alan
Sutcliffe calls it "the heart of the
301:, reviewer M. H. Greenblatt writes that its inclusion of exercises and problems makes it feel "much more like a text book", but not in a negative way. Similarly, Alan Sutcliffe writes that "an almost ideal balance has been struck between educational and recreational", and
294:
mathematicians, mathematics educators, and amateurs" interested in recreational mathematics. Senger adds that the second edition is especially welcome because of the difficulty of finding a copy of the out-of-print first edition.
204:
book", and an essential bridge between the earlier and later chapters. The question of using these methods to find a formula for the number of polyominoes with a given number of squares remains unsolved, and central to the topic.
231:
on the smallest rectangles that can be tiled by certain polyominoes, and another chapter summarizing other recent work on polyominoes and polyomino tiling, including the
263:
186:
283:
227:
of certain tiling problems including the problem of whether a set of polyominoes can tile the plane. The second edition adds a chapter on the work of
623:
28:
100:
70:
672:
232:
123:. The book's title word "polyominoes" was invented for the subject by Golomb in 1954 as a back-formation from "domino".
195:
methods for searching for polyomino tilings or proving their nonexistence, and the fifth introduces techniques from
667:
138:
reprinting a report by Andy Liu of the solution to all open problems proposed in an appendix to the first edition.
111:
The book collects together material previously published by Golomb in various articles and columns, especially in
196:
298:
96:
130:, was published by Mir in 1975; it includes also translations of two papers on polyominoes by Golomb and by
236:
162:(made from five squares), the rectangular shapes that can be formed from them, and the subsets of an
224:
220:
200:
662:
606:
554:
493:
447:
410:
192:
242:
165:
617:
65:
647:
580:
519:
485:
402:
131:
340:
584:
523:
336:
216:
469:
302:
268:
92:
207:
The final two chapters of the first edition concern generalizations of polyominoes to
656:
228:
353:
640:
120:
88:
103:
has strongly recommended its inclusion in undergraduate mathematics libraries.
159:
146:
84:
212:
208:
155:
610:
558:
451:
154:
After an introductory chapter that enumerates the polyominoes up to the
497:
414:
158:(made from six squares), the next two chapters of the book concern the
489:
406:
115:. It was originally published by Scribner's in 1965, titled simply
145:
305:
calls its coverage of the topic "fascinating and thorough".
188:
chessboard into which the twelve pentominoes can be packed.
265:
rectangles must have a side whose length is a multiple of
22:
Polyominoes: Puzzles, Patterns, Problems, and
Packings
80:
Polyominoes: Puzzles, Patterns, Problems, and
Packings
271:
245:
168:
64:
54:
46:
38:
277:
257:
180:
87:, the shapes formed by connecting some number of
434:Greenblatt, M. H. (September 1965), "Review of
95:, and is "universally regarded as a classic in
541:Senger, Elizabeth (January 1997), "Review of
33:Revised and Expanded second edition (English)
8:
429:
427:
425:
423:
389:Sutcliffe, Alan (November 1965), "Review of
119:, and including a plastic set of the twelve
21:
384:
382:
380:
378:
376:
374:
372:
99:". The Basic Library List Committee of the
27:
20:
464:
462:
460:
270:
244:
167:
126:A translation into Russian by I. Yaglom,
536:
534:
532:
322:
320:
318:
314:
615:
327:Martin, George E. (1995), "Review of
7:
622:: CS1 maint: untitled periodical (
101:Mathematical Association of America
597:Hale, Elaine M. (September 1995),
239:that a rectangle tiled by smaller
215:, and briefly mention the work of
18:Book on shapes formed from squares
14:
113:Recreational Mathematics Magazine
91:edge-to-edge. It was written by
1:
571:De Clerck, Frank, "Review of
191:The fourth chapter discusses
233:mutilated chessboard problem
510:Stefanescu, M., "Review of
472:(October 1968), "Review of
297:Although the book concerns
689:
50:Princeton University Press
258:{\displaystyle 1\times n}
197:enumerative combinatorics
181:{\displaystyle 8\times 8}
83:is a mathematics book on
26:
478:The Mathematical Gazette
299:recreational mathematics
97:recreational mathematics
599:The Mathematics Teacher
547:The Mathematics Teacher
673:1965 non-fiction books
289:Audience and reception
279:
259:
182:
151:
150:The twelve pentominoes
280:
260:
183:
149:
395:Mathematics Magazine
333:Mathematical Reviews
269:
243:
166:
237:De Bruijn's theorem
107:Publication history
23:
440:American Scientist
275:
255:
193:brute-force search
178:
152:
668:Mathematics books
278:{\displaystyle n}
76:
75:
680:
648:Internet Archive
628:
627:
621:
613:
594:
588:
587:
568:
562:
561:
538:
527:
526:
514:(Russian ed.)",
507:
501:
500:
466:
455:
454:
446:(3): 356A–357A,
431:
418:
417:
386:
367:
366:
365:
364:
350:
344:
343:
324:
284:
282:
281:
276:
264:
262:
261:
256:
201:Burnside's lemma
187:
185:
184:
179:
132:David A. Klarner
56:Publication date
31:
24:
688:
687:
683:
682:
681:
679:
678:
677:
653:
652:
637:
632:
631:
614:
596:
595:
591:
570:
569:
565:
540:
539:
530:
509:
508:
504:
490:10.2307/3614210
470:Liebeck, Pamela
468:
467:
458:
433:
432:
421:
407:10.2307/2687945
388:
387:
370:
362:
360:
352:
351:
347:
326:
325:
316:
311:
291:
267:
266:
241:
240:
217:Edward F. Moore
164:
163:
144:
109:
57:
34:
19:
12:
11:
5:
686:
684:
676:
675:
670:
665:
655:
654:
651:
650:
636:
635:External links
633:
630:
629:
589:
563:
528:
502:
456:
419:
401:(5): 313–314,
368:
345:
313:
312:
310:
307:
303:Pamela Liebeck
290:
287:
274:
254:
251:
248:
225:undecidability
177:
174:
171:
143:
140:
108:
105:
93:Solomon Golomb
74:
73:
68:
62:
61:
58:
55:
52:
51:
48:
44:
43:
42:Solomon Golomb
40:
36:
35:
32:
17:
13:
10:
9:
6:
4:
3:
2:
685:
674:
671:
669:
666:
664:
661:
660:
658:
649:
645:
643:
639:
638:
634:
625:
619:
612:
608:
604:
600:
593:
590:
586:
582:
578:
574:
567:
564:
560:
556:
552:
548:
544:
537:
535:
533:
529:
525:
521:
517:
513:
506:
503:
499:
495:
491:
487:
483:
479:
475:
471:
465:
463:
461:
457:
453:
449:
445:
441:
437:
430:
428:
426:
424:
420:
416:
412:
408:
404:
400:
396:
392:
385:
383:
381:
379:
377:
375:
373:
369:
359:
355:
354:"Polyominoes"
349:
346:
342:
338:
334:
330:
323:
321:
319:
315:
308:
306:
304:
300:
295:
288:
286:
272:
252:
249:
246:
238:
234:
230:
229:David Klarner
226:
222:
218:
214:
210:
205:
202:
198:
194:
189:
175:
172:
169:
161:
157:
148:
141:
139:
135:
133:
129:
124:
122:
118:
114:
106:
104:
102:
98:
94:
90:
86:
82:
81:
72:
71:9780691024448
69:
67:
63:
59:
53:
49:
45:
41:
37:
30:
25:
16:
641:
602:
598:
592:
576:
575:(2nd ed.)",
572:
566:
550:
546:
545:(2nd ed.)",
542:
515:
511:
505:
484:(381): 306,
481:
477:
476:(1st ed.)",
473:
443:
439:
438:(1st ed.)",
435:
398:
394:
393:(1st ed.)",
390:
361:, retrieved
357:
348:
332:
331:(2nd ed.)",
328:
296:
292:
223:proving the
206:
190:
153:
136:
127:
125:
116:
112:
110:
89:unit squares
79:
78:
77:
15:
642:Polyominoes
573:Polyominoes
543:Polyominoes
512:Polyominoes
474:Polyominoes
436:Polyominoes
391:Polyominoes
358:MAA Reviews
329:Polyominoes
160:pentominoes
121:pentominoes
117:Polyominoes
85:polyominoes
657:Categories
605:(6): 524,
585:0831.05020
524:0326.05025
363:2020-06-19
309:References
211:and other
199:including
156:hexominoes
663:Polyforms
644:(2nd ed.)
553:(1): 72,
250:×
213:polyforms
209:polycubes
173:×
47:Publisher
618:citation
611:27969460
559:27970078
452:27836143
221:Hao Wang
128:Полимино
646:on the
498:3614210
415:2687945
341:1291821
609:
583:
577:zbMATH
557:
522:
516:zbMATH
496:
450:
413:
339:
142:Topics
39:Author
607:JSTOR
555:JSTOR
494:JSTOR
448:JSTOR
411:JSTOR
624:link
235:and
219:and
66:ISBN
60:1965
581:Zbl
520:Zbl
486:doi
403:doi
659::
620:}}
616:{{
603:88
601:,
579:,
551:90
549:,
531:^
518:,
492:,
482:52
480:,
459:^
444:53
442:,
422:^
409:,
399:38
397:,
371:^
356:,
337:MR
335:,
317:^
285:.
134:.
626:)
488::
405::
273:n
253:n
247:1
176:8
170:8
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
