The Zen of Magic Squares, Circles, and Stars

Product Description

Humanity’s love affair with mathematics and mysticism reached a critical juncture, legend has it, on the back of a turtle in ancient China. As Clifford Pickover briefly recounts in this enthralling book, the most comprehensive in decades on magic squares, Emperor Yu was supposedly strolling along the Yellow River one day around 2200 B.C. when he spotted the creature: its shell had a series of dots within squares. To Yu’s amazement, each row of squares contained fifteen dots, as did the columns and diagonals. When he added any two cells opposite along a line through the center square, like 2 and 8, he always arrived at 10. The turtle, unwitting inspirer of the “Yu” square, went on to a life of courtly comfort and fame. 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. 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.

Review

“Pickover writes about his subject with contagious enthusiasm and comprehensive erudition.”,
Choice

“Clifford Pickover is many things–scientist, scholar, author, editor, and visionary.”,
Games

“Through accessible and readable prose and through detailed, highquality line illustrations, Pickover ably transports the general reader from culturally embedded traditional topics to a new and surprising frontier.”
—Harold Don Allen, Mathematics Teacher

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

“It is a safe bet to conjecture that this is the best recreational mathematics book that will be published in this year. . . . Pickover writes with his usual style and straightforward simplicity in this book. The material is presented well and can be understood by anyone with a basic middle school mathematics background. This is a cool book!”
—Charles Ashbacker, Journal of Recreational Mathematics

“A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today.”,
Journal of Recreational Mathematics

“Pickover just seems to exist in more dimensions than the rest of us.”
—Ian Stewart, Scientific American

Review

“At first glance magic squares may seem frivolous (Ben Franklin’s opinion, even as he spent countless hours studying them!), but I think that is wrong. The great nineteenth-century German mathematician Leopold Kronecker said ‘God Himself made the whole numbers―everything else is the work of men,’ and Cliff Pickover’s stimulating book hints strongly at the possibility that God may have done more with the integers than just create them. I don’t believe in magic in the physical world, but magic squares come as close as we will probably ever see to being mathematical magic.”
―Paul J. Nahin, University of New Hampshire, author of Duelling Idiots and Other Probability Puzzlers

From the Back Cover

“A refreshing new look at a timeless topic, brimming over with ideas, littered with surprising twists. Anyone who loves numbers, anyone who enjoys puzzles, will find The Zen of Magic Squares, Circle