Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks

Synopsis

Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath Principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem.

Diaconis and Graham are mathematicians as well as skilled performers with decades of professional experience between them. In this book they share a wealth of conjuring lore, including some closely guarded secrets of legendary magicians. Magical Mathematics covers the mathematics of juggling and shows how the I Ching connects to the history of probability and magic tricks both old and new. It tells the stories--and reveals the best tricks--of the eccentric and brilliant inventors of mathematical magic. Magical Mathematics exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card monte, traces the history of mathematical magic back to the thirteenth century and the oldest mathematical trick--and much more.

Excerpt

If you are not familiar with the strange, semisecret world of modern conjuring you may be surprised to know that there are thousands of entertaining tricks with cards, dice, coins, and other objects that require no sleight of hand. They work because they are based on mathematical principles.

Consider, for example, what mathematicians call the Gilbreath Principle, named after Norman Gilbreath, its magician discoverer. Arrange a deck so the colors alternate, red, black, red, black, and so on. Deal the cards to form a pile about equal to half the deck, then riffle shuffle the piles together. You’ll be amazed to find that every pair of cards, taken from the top of the shuffled deck, consists of a red card and a black card! Dozens of beautiful card tricks—the best are explained in this marvelous book—exploit the Gilbreath Principle and its generalizations.

Although you can astound friends with tricks based on this principle, they are in this book for another reason. the principle turned out to have applications far beyond trivial math. For example, it is closely related to the famous Mandelbrot set, an infinite fractal pattern generated on a computer screen by a simple formula.

But that is not all. the Dutch mathematician N. G. de Bruijn discovered that the Gilbreath principle applies to the theory of Penrose tiles (two shapes that tile the plane only in a nonperiodic way) as well as to the solid form of Penrose tiles, which underlies what are called quasicrystals. Still another application of the principle, carefully explained in this book, is to the design of computer algorithms for sorting procedures.

The authors are eminent mathematicians. Ron Graham, retired from Bell Labs and now a professor at the University of California, San Diego, is an expert on combinatorial math. Persi Diaconis is an equally . . .

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