## Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks

Author(s): Persi Diaconis

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Magical Mathematics reveals the secrets of 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. Diaconis and Graham tell the stories--and reveal the best tricks--of the eccentric and brilliant inventors of mathematical magic. The book 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 oldest mathematical trick--and much more.

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Winner of the 2013 Euler Book Prize, Mathematical Association of America Honorable Mention for the 2012 Award for Best Professional/Scholarly Book in Popular Science & Popular Mathematics, Association of American Publishers "[F]ascinating... Magical Mathematics [is] a dazzling tour of math-based magic tricks... Lovers of recreational mathematics, and especially fans of the late Martin Gardner, who contributed the foreword, will find many pleasures in Magical Mathematics. And while exposing magic secrets in a book intended for the general public may raise hackles among some old-guard magicians, exploring the math behind these tricks will, in truth, only deepen the mystery. For, as the authors remind us, sometimes the methods are as magical as the tricks themselves."--Alex Stone, Wall Street Journal "The Riemann hypothesis, the Mandelbrot set, Fermat's last theorem--these mathematical notions and others underlie all manner of magic tricks. Mathematicians Persi Diaconis--also a card magician--and Ron Graham--also a juggler--unveil the connections between magic and math in this well-illustrated volume."--Scientific American "Writing for the public, the two authors share their passions, teaching sophisticated mathematical concepts along with interesting card tricks, which rely upon those principles for their workings."--GENII: The Conjurors' Magazine "[I]t is simply a beautiful book. The design, layout, typography, even the paper is beautiful... [T]his is one of the most fun, engaging new popular mathematics books I've seen in a long time."--The Math Less Traveled Blog "The authors are master storytellers... [T]he authors offer advice and recommendations for further pursuits in mathematics, magic and juggling."--Cut-the-Knot blog "Well known and highly respected in the mathematical community, Diaconis and Graham have produced a work that completely lives up to expectations. It contains descriptions of magic tricks as viewed by an audience, the mathematics that make them possible, and clear explanations to help you--with a little practice--amaze your friends."--Library Journal "Magical Mathematics gives readers a peek behind the velvet curtain that hides the magician's secrets... The book covers some nifty card tricks, juggling, codes and a slew of mind-bending puzzles. The book doesn't just tell you how to fool and impress your friends with parlour tricks, it explains why these tricks work, so that you can go on to devise your own--in fact, the authors challenge you to do just that. The writing is lively and the tricks are well set-up, providing newbie magicians with both points of view: what the audience sees and what the magician knows."--Montreal Gazette "Magical Mathematics is an absolutely remarkable book. I don't say this lightly. Publishers send me plenty of books to review. Some I like more than others. Magical Mathematics is a fantastic book for someone who wants to explore the non-trivial math behind some impressive magic tricks. While I enjoy purely recreational math puzzles that have no practical application I also love it when I discover challenges that are interesting and relevant. Magical Mathematics is chock full of fun (and deep) challenges that students (and adults) can sink their teeth into."--Wild About Math blog "Over 12 chapters, the reader is taken on a unique and wonderful tour that fuses magical tricks with underlying mathematical explanations and personal stories, written by world-renowned experts in both fields. With its friendly, disarming style, the book is pitched perfectly at a level that will surprise both the hardened mathematical researcher and the interested general reader, without putting either of them off... [T]his book is a must-buy."--C.J. Howls, Times Higher Education Supplement "The first chapter of this book begins by teaching a simple four-card trick and ends by presenting--complete with step-by-step color illustrations--a more complicated card trick that will truly amaze any audience. Both tricks are based on mathematical principles, and the book goes on to explain these and many other principles that can be the basis for a variety of clever magic tricks."--Games magazine "Learn the secrets behind card tricks, including step-by-step instructions for performing them, along with the mathematical ideas the tricks illustrate."--Science News "As magic books go, Magical Mathematics is erudite, thought provoking, inspiring... It is the product of multiple decades of work and research, and for a small subset of magic enthusiasts it could rank as the best book they buy this decade."--James Alan, Magicol "There is so much to digest in this book that it is impossible to describe even a fraction of it in just a few paragraphs. Let it suffice to say that if you are at all interested in card magic principles, how they work, why they work, and the history behind them, to ignore this book would be a serious mistake."--Peter Duffie, Magic magazine "From arcane theories to practical tips for working magicians, the authors go behind the curtain and reveal how the pros do it."--San Jose Mercury News "The connection between magic and mathematics has a long and intriguing history, and throughout their book Diaconis and Graham present detailed and fascinating insight into that history... Overall, the book is a wonderful introduction to this esoteric area, but has more than enough depth to entertain and enlighten the knowledgeable. Perhaps most important of all, it shows how deconstructing illusion can provide fascinating insight in the nature of reality."--Richard Wiseman, Nature Physics "Magical Mathematics strikes a nice balance between descriptions of performable magic tricks and the mathematics that makes them work. Unlike some 'mathemagic' books, in this work, Diaconis and Graham describe magic tricks that are actually used by professionals... [T]he writing is engaging, and learning the tricks that are presented is well worth the effort... This volume should find a place in any mathematics or magic library collection."--Choice "While turning the last pages, the reader is bound to feel touched and charged up and would definitely be moving in an altered direction, for this is a book that will not just leave an impression, but will also suggest which path to take next."--Shubashree Desikan, Current Science "Reading Magical Mathematics ... had ... [a] powerful effect on me. I was transported to a strange and shadowy world of card tricks and magic that, at the same time, was miraculously a land of mathematics, a land with substance... Barely ten pages into the book I am completely hooked."--John J Watkins, Mathematical Reviews "The authors have produced an invaluable contribution to the fascinating relationship between magic and mathematics... The authors exhibit a lifelong passion, enthusiasm and deep knowledge for magic and mathematics and this is an ideal combination for producing a great read... I highly recommend it to anybody interested in the mathematics behind some impressive magic."--Fiacre O. Cairbre, Irish Mathematical Society Bulletin "Mathematical Magic is a truly magical book, containing ample amounts of mathematics and magic that will amaze and amuse. Diaconis and Graham are both first-rate mathematicians and performers and offer insights and ideas that could not have been expressed by anyone else. This book is destined to be a classic on the subject."--Arthur Benjamin, SIAM "This is a splendid book with lots of wonderful insights... Give this book a try; you certainly will not be disappointed."--Phil Dyke, Leonardo Reviews "While there are other books out there detailing the relationship between mathematics and magic, this book is perhaps the best written of them all, as it will appeal to magicians, math buffs and general readers alike."--R. S. Beer, MagicBookReviews.com

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

### General Fields

- :
- : Princeton University Press
- : Princeton University Press
- : October 2015
- : 241mm X 216mm
- : United States
- : books

### Special Fields

- : Persi Diaconis
- : Paperback
- : 510
- : 264
- : 133 color illus. 14 halftones. 56 line illus. 10 tables.