Magical Mathematics

Persi Diaconis is professor of mathematics and statistics at Stanford University and a professional magician. Ron Graham is professor of mathematics and computer science at the University of California, San Diego, and a professional juggler.

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