## Across the Board: |

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, "This book is extremely well written and is, no doubt, the best exposition of the connection between the chessboard problems and recreational mathematics. The author surveys all the well-known problems about chess and the chessboard. . . . The problems are treated in depth from their beginnings through to their status today." "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." "Watkins offers an excellent invitation to serious mathematics." "I would be happy to recommend this book to you. . . . The book is an easy and entertaining read that shows numerous paths into various branches of discrete mathematics and graph theory." "This is not just about chess, but also the three centuries of 'recreational mathematics' that the game has inspired. From simple questions, such as whether it is possible for a knight to land on each square of the board on its path, Watkins wades into graph theory, the mathematics of three-dimensional chess and even chess on a torus." Preface ix
- Dutch
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