Across the board : the mathematics of chessboard problems / John J. Watkins.

Format:

Book

Author/Creator:

Watkins, John J.

Series:

Princeton Puzzlers

Language:

English

Subjects (All):

Mathematical recreations.

Chess.

Physical Description:

1 online resource (270 p.)

Edition:

Course Book

Place of Publication:

Princeton : Princeton University Press, c2004.

Language Note:

English

Summary:

Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens? Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery. Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

Contents:

Frontmatter

Contents

Preface

Chapter One. Introduction

Chapter Two. Knight's Tours

Chapter Three. The Knight's Tour Problem

Chapter Four. Magic Squares

Chapter Five. The Torus and the Cylinder

Chapter Six. The Klein Bottle and Other Variations

Chapter Seven. Domination

Chapter Eight. Queens Domination

Chapter Nine. Domination on Other Surfaces

Chapter Ten. Independence

Chapter Eleven. Other Surfaces, Other Variations

Chapter Twelve. Eulerian Squares

Chapter Thirteen. Polyominoes

References

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 247-249) and index.

ISBN:

9786613256065

9781283256063

1283256061

9780691115030

0691115036

9781400840922

1400840929

OCLC:

749265026