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Publisher:

Princeton University Press

Publication Date:

2011

Number of Pages:

244

Format:

Hardcover

Price:

29.95

ISBN:

9780691151649

Category:

General

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by , on ]

John D. Cook

11/3/2011

If you wanted to find a perfect book on magic and mathematics, you might look for something written by Persi Diaconis and Ron Graham. The only thing more you might ask would be a preface by the late Martin Gardner. *Magical Mathematics* is precisely that book.

As the title suggests, *Magical Mathematics* is indeed a book about magic and mathematics. Not obvious from the title is that the book also contains a significant amount of biography, which we will say more of in a moment. The mathematics in the book is mostly elementary. The book is aimed at a popular audience, not professional mathematicians. However, Diaconis and Graham allude to much deeper mathematical connections that are not explicitly developed in their book.

All the magic in the book has mathematical explanations; none of the tricks depend on slight of hand or tricky equipment. But rather than simply giving dry, mathematical descriptions, each trick is presented with sample patter and notes on showmanship.

The mathematics and the magic are intertwined. Magic tricks suggest mathematical problems, and mathematical solutions suggest magic tricks. Sometimes an innovation on one side spurs an innovation on the other side.

In addition to instruction in magic and mathematics, *Magical Mathematics* tells stories of mathematical magicians, including some who influenced the authors. Chapter 7, for example, begins with a story from Diaconis’ childhood and ends with a story Graham’s. (The authors do not clearly identify themselves; it takes a little deduction to determine which is speaking when the book includes personal anecdotes.)

*Magical Mathematics*, like the careers of its authors, blurs the lines between “serious” and “recreational” mathematics.

John D. Cook is a research statistician at M. D. Anderson Cancer Center and blogs daily at The Endeavour.

Foreword ix

Preface xi

Chapter 1: Mathematics in the Air 1

Royal Hummer 8

Back to Magic 15

Chapter 2: In Cycles 17

The Magic of de Bruijn Sequences 18

Going Further 25

Chapter 3: Is This Stuff Actually Good For Anything? 30

Robotic Vision 30

Making Codes 34

To the Core of Our Being 38

This de Bruijn Stuff Is Cool but Can It Get You a Job? 42

Chapter 4: Universal Cycles 47

Order Matters 47

A Mind-reading Effect 52

Universal Cycles Again 55

Chapter 5: From the Gilbreath Principle to the Mandelbrot Set 61

The Gilbreath Principle 61

The Mandelbrot Set 72

Chapter 6: Neat Shuffles 84

A Mind-reading Computer 85

A Look Inside Perfect Shuffles 92

A Look Inside Monge and Milk Shuffles 96

A Look Inside Down-and-Under Shuffles 98

All the Shuffles Are Related 99

Chapter 7: The Oldest Mathematical Entertainment? 103

The Miracle Divination 105

How Many Magic Tricks Are There? 114

Chapter 8: Magic in the Book of Changes 119

Introduction to the Book of Changes 121

Using the I Ching for Divination 122

Probability and the *Book of Changes* 125

Some Magic (Tricks) 127

Probability and the I Ching 136

Chapter 9: What Goes Up Must Come Down 137

Writing It Down 138

Getting Started in Juggling 145 10 Stars of Mathematical Magic (and some of the best tricks in the book) 153

Alex Elmsley 156

Bob Neale 160

Henry Christ 173

Stewart James 181

Charles Thornton Jordan 189

Bob Hummer 201

Martin Gardner 211

Chapter 11: Going further 220

Chapter 12: on secrets 225

Notes 231

Index 239

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