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John J. Watkins, "Across the Board: The Mathematics of Chessboard Problems"

Here is a chess book that homes in on the properties of the chessboard itself. College professor Watkins informs readers that the chessboard and chess pieces can be analyzed in terms of graph theory, which has real-world relevance--to the structure of communications networks, for example. And Watkins indeed sets up his tour of chess-qua-graph theory as a collection of problems to be solved, and theorems to be proven, all on the difficulty level one encounters in Scientific American's popular feature "Mathematical Games." When he was a teenager, comments Watkins, that column alerted him to the chessboard's mathematical intricacies, which encompass the number of squares a piece can move to or control, with variations extending to boards of different sizes and shapes. 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.

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