Polyominoes: Puzzles, Patterns, Problems, and Packings - Revised and Expanded Second Edition

by Solomon W. Golomb

Overview

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.

Product Details

ISBN-13:	9780691024448
Publisher:	Princeton University Press
Publication date:	04/07/1996
Series:	Princeton Science Library , #16
Edition description:	Revised and Expanded Second
Pages:	198
Sales rank:	659,120
Product dimensions:	7.75(w) x 10.00(h) x (d)

About the Author

Solomon W. Golomb, University Professor at the University of Southern California, teaches in the Departments of Mathematics and Electrical Engineering, invents mathematical puzzles, and publishes in many areas of science and technology.

Table of 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	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

What People are Saying About This

Martin Gardner

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"

From the Publisher

"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

Editorial Reviews

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

Journal of Recreational Mathematics

The book covers all areas, both beginner and expert, thoroughly. Hundreds of diagrams illustrate the detailed, clearly written texts.... A classic. From a simple idea, Golomb has created a ... science.

New Scientist - Colin Singleton

One of the most eagerly anticipated second editions in the history of mathematics, [Polyominoes] was worth it.... Truly a jewel in the crown of mathematical royalty, this book deserves to be a runaway bestseller.

Journal of Recreational Mathematics - Charles Ashbacher

The book covers all areas, both beginner and expert, thoroughly. Hundreds of diagrams illustrate the detailed, clearly written texts.... A classic. From a simple idea, Golomb has created a ... science.
— Colin Singleton

New Scientist

"The book covers all areas, both beginner and expert, thoroughly. Hundreds of diagrams illustrate the detailed, clearly written texts.... A classic. From a simple idea, Golomb has created a ... science."—-Colin Singleton, New Scientist

"One of the most eagerly anticipated second editions in the history of mathematics, [Polyominoes] was worth it.... Truly a jewel in the crown of mathematical royalty, this book deserves to be a runaway bestseller."—-Charles Ashbacher, Journal of Recreational Mathematics

From the Publisher