The Zen of Magic Squares, Circles, and Stars

“It is a safe bet to conjecture that this is the best recreational mathematics book that will be published in this year . . . a cool book!” —Charles Ashbacker, Journal of Recreational Mathematics

In this “refreshing new look at a timeless topic,” Clifford Pickover explains why Chinese emperors, Babylonian astrologer-priests, prehistoric cave people in France, and ancient Mayans of the Yucatan were convinced that magic squares—arrays filled with numbers or letters in certain arrangements—held the secret of the universe (Ian Stewart, author of In Pursuit of the Unknown). Since the dawn of civilization, he writes, humans have invoked such patterns to ward off evil and bring good fortune. Yet who would have guessed that in the twenty-first century, mathematicians would be studying magic squares so immense and in so many dimensions that the objects defy ordinary human contemplation and visualization?

Readers are treated to a colorful history of magic squares and similar structures, their construction, and classification along with a remarkable variety of newly discovered objects ranging from ornate inlaid magic cubes to hypercubes. Illustrated examples occur throughout, with some patterns from the author's own experiments. The tesseracts, circles, spheres, and stars that he presents perfectly convey the age-old devotion of the math-minded to this Zenlike quest. Number lovers, puzzle aficionados, and math enthusiasts will treasure this rich and lively encyclopedia of one of the few areas of mathematics where the contributions of even nonspecialists count.

“A splendid recreational book . . . An extremely alluring page-turner.” —Andrew Bremner, Notices of the American Mathematical Society