Archimedes' Revenge: The Joys and Perils of Mathematics by Paul E. Hoffman
	(Illus.) W.W. Norton & Company, Incorporated 1989 viii + 285 pp. 0-449-21750-7 Index C-T, GA **

Martin Gardner's column in Scientific American on mathematical puzzles is well known, and this book is very much in that genre. Rather than posing puzzles to be solved, however, Hoffman describes the solutions to famous mathematical puzzles, beginning with a diabolical one attributed to Archimedes that was solved only recently with the aid of modern computers. The 4 parts of the book are: numbers, shapes, machines, and one man, one vote. The 13 chapters range from "Archimedes' Revenge" to "The Cryptic Case of a Swarthy Stranger" to "Adventures of an Egg Man," "The Mobius Molecule," "The Case of the Missing Three-Hold Hollow Sphere with One Handle," "Is Democracy Mathematically Unsound," and "The Quantum Congress." Entertaining and intriguing, this book provides a mix of ancient history and very recent events. Perhaps the most appealing aspect is that Hoffman makes all the problems--ancient and modern--accessible to readers without placing heavy demands on their background. Not intended as a textbook, this book might well serve as a principal resource for a liberal arts course. Elementary and high school teachers will enjoy it as well. It might even prove to be accessible to high school students.

--Reviewed by Donald E. Myers in Science Books and Films, 24/3 (January/February 1989), p. 138.