Across The Board: The Mathematics of Chessboard Problems

Across The Board: The Mathematics of Chessboard Problems

Ref: c3062

"Torus-shaped boards, three-dimensional boards, a shape called the Klein bottle--the simple checkerboard pattern proves to be creatively malleable when Watkins puts his mind to his hobbylike subject. Watkins' invitational tone ensures attention from the finite but enthusiastic audience for mathematical recreation."--Booklist

"This beautiful book is absolutely the best treatment of the connection between chess and recreational mathematics I have ever seen. What makes it stand apart (and far above) other chess puzzle books is the underlying mathematical theory, presented in an entertaining, fascinating, and educational manner."--Paul J. Nahin, author of When Least Is Best

"Watkins has a friendly writing style, and the reader is brought along nicely from simple concepts to slightly more complicated ones."--Ron Graham, 2003 Steele Prize for Lifetime Achievement, American Mathematical Society, and President, Mathematical Association of America

Table of Contents:
Preface ix
Chapter One: Introduction 1
Chapter Two: Knight's Tours 25
Chapter Three: The Knight's Tour Problem 39
Chapter Four: Magic Squares 53
Chapter Five: The Torus and the Cylinder 65
Chapter Six: The Klein Bottle and Other Variations 79
Chapter Seven: Domination 95
Chapter Eight: Queens Domination 113
Chapter Nine: Domination on Other Surfaces 139
Chapter Ten: Independence 163
Chapter Eleven: Other Surfaces, Other Variations 191
Chapter Twelve: Eulerian Squares 213
Chapter Thirteen: Polyominoes 223
References 247
Index 251