Across the Board: The Mathematics of Chessboard Problems

Across the Board: The Mathematics of Chessboard Problems

by John J. Watkins
     
 

ISBN-10: 0691115036

ISBN-13: 9780691115030

Pub. Date: 03/01/2004

Publisher: Princeton University Press

"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…  See more details below

Overview

"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 fertile area of recreational mathematics." 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.

Product Details

ISBN-13:
9780691115030
Publisher:
Princeton University Press
Publication date:
03/01/2004
Series:
Princeton Puzzlers Series
Pages:
272
Product dimensions:
6.40(w) x 9.44(h) x 0.98(d)

Table of Contents

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.

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