Polyominoes: Puzzles, Patterns, Problems, and Packings [Hardcover]

Solomon W. Golomb (Author), Warren Lushbaugh (Illustrator)

Book Description

Publication Date: September 6, 1994 | ISBN-10: 0691085730 | ISBN-13: 978-0691085739 | Edition: 2nd

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.

Editorial Reviews

Review

Truly a jewel in the crown of mathematical royalty, this book deserves to be a runaway bestseller.

From the Back Cover

"Those acquainted with polyominoes will snap up this volume. And if you haven't yet discovered the fascination of these tantalizing tiles, this is the book to introduce you to them . . . ."--Martin Gardner, author of The Ambidextrous Universe

--This text refers to the Paperback edition.

Product Details

• Hardcover: 184 pages
• Publisher: Princeton University Press; 2nd edition (September 6, 1994)
• Language: English
• ISBN-10: 0691085730
• ISBN-13: 978-0691085739
• Product Dimensions: 9.4 x 6.2 x 1.1 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,961,332 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 12 people found the following review helpful:

5.0 out of 5 stars Even better the second time through, June 29, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Polyominoes: Puzzles, Patterns, Problems, and Packings (Paperback)

One of the most eagerly anticipated second editions in the history of mathematics, the wait was worth it. Literally defining a whole new area of recreational mathematics, the problems and proof techniques introduced in the first edition have kept an entire generation of mathematical thinkers busy. Although easily understood, some of the problems have defied solution for decades after the publication of the first edition in 1965. It now appears that all of the problems listed as unsolved in the first edition have been resolved, the last succumbing in 1993. As befits the enormous interest in these problems, three people announced solutions simultaneously, this reviewer being one of them.
While there is not a lot of material that was not part of the first book, it still stirs the mathematical heart. For these problems and proofs are timeless things of beauty. Even a child can understand how to put polyominoes together - my two-year-old daughter is an existence proof of that. And the proofs are sometimes so clever in their simplicity that one is tempted to use the phrase attributed to Paul Erdos, "That one is from God's little book." Who among us fails to appreciate some of the proofs of placing pentominoes on a checkerboard that relies on nothing more than the number of spaces colored black versus red. Even the proofs of the problems that took decades to resolve can be understood by those with only a rudimentary knowledge of mathematics. Sometimes, if you can count to 60, you can understand the proof.
Truly a jewel in the crown of mathematical royalty, this book deserves to be a runaway bestseller.

Published in Journal of Recreational Mathematics, reprinted with permission

3 of 3 people found the following review helpful:

5.0 out of 5 stars Ultimate book on polyominoes by the inventor., February 16, 2002

By 

anon2001 "anon2001" (Kinross, Western Australia AUSTRALIA) - See all my reviews

This review is from: Polyominoes: Puzzles, Patterns, Problems, and Packings (Paperback)

Polyominoes is an entire sub-domain of geometrical puzzles and
this book is the epitomie of the subject. Packed full of
results and puzzles old and new. An extensive bibliography
is provided. Another one for the bookshelf of all mathematical puzzlers.