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By Root 733 0

Stefan Mandel, Robert Lang, David Bellos and Ilona Morison. And thanks also to Natalie Hunt, Simon Veksner, Veronica Esaulova, Gavin Pretor-Pinney, Justin Leighton, Jeannine Mosely, Ravi Apte, Hugo de Klee, Maura O’Brien, Peter Dawson, Paul Palmer-Edwards, Elaine Leggett, Rebecca Folland, Kirsty Gordon, Tim Glister, Hugh Morison, Jonathan Cummings, Raphael Zarum, Mike Keith, Gareth Roberts, Gene Zirkel, Erik Demaine, Wayne Gould, Kirk Pearson, Angela Newing, Bill Eadington, Mike LeVan, Sheena Russell, Hartosh Bal, Ivan Moscovich, John Holden, Chris Ottewill, Mariana Kawall Leal Ferreira, Todd Rangiwhetu, William Poundstone, Frank Swetz and Amir Aczel. And lastly, Zara Bellos, my niece, who has promised to get an A star in maths if I mention her somewhere in these pages.

Picture Credits

p. 26 © Tetsuro Matsuzawa.

p. 48 Courtesy of Jürg Wassmann.

pp. 50–55 Doz

enal fonts and DSAgo courtesy of Michael de Vlieger, Dozenal Society of America.

p. 59 From the collection of the Musée international d’horlogerie, La Chaux-de-Fonds, Switzerland.

p. 101 © Sir Roger Penrose.

p. 106 © Ravi Apte.

p. 189 Science Museum/Science & Society Picture Library.

p. 193 Science Museum/Science & Society Picture Library.

p. 210 © Justin Leighton.

p. 214 © Maki Kaji.

p. 220 © Jose/Fotolia.

p. 221 Courtesy of the Clendening History of Medicine Library, University of Kansas Medical Center.

p. 232 Courtesy of Jerry Slocum.

p. 235 Courtesy of Jerry Slocum.

pp. 238–9 Get Off The Earth is a registered trademark of the Sam Loyd Company and used by permission.

p. 244 Reproduced with permission of Scott Kim.

p. 245 Courtesy of Mark Palmer, Wow Tattoos.

p. 250 © Dániel Erdély, Walt van Ballegooijen and the Spidron Team, 2008. Artwork: Dániel Erdély.

p. 270 Courtesy of Paul Bateman.

p. 286 Used under license from Shutterstock.com.

p. 294 Kasia, 2009. Used under license from Shutterstock.com.

p. 301 © Alex Bellos.

p. 316 Scott W. Klette, courtesy of Nevada State Museum, Carson City, NV.

p. 344 Courtesy William Poundstone.

p. 384 © Daina Taimina.

p. 393 © The M.C. Escher Company, Holland, 2009. All rights reserved. www.mcescher.com.

p. 396 © Daina Taimina.

*In fact, numbers need to get closer in a certain way for the scale to be logarithmic. For a fuller discussion of the scale

,

*A group of eight divinities in the Indian epic the Mahabharata.

*The mathematical constant e is an irrational number beginning 2.718281828, which Gregory Chudnovsky calls ‘twice Tolstoy’ since the Russian novelist was born in 1828. It has no relation to Einstein’s equation E=mc 2, where E means energy.

*In the original, the spelt figure is mistakenly written 2301.

2">†Egyptian unit of volume.

*Using the convention that 00 = 1, since if 00 = 0 the number would collapse immediately.

*The definition of the sequence appears as an appendix

.

*You might think that lines of latitude are parallel to the equator. This is not true because the lines of latitude (with the exception of the equator) are not straight lines, and only straight lines can be parallel to each other. A straight line is the shortest distance between two points, which is why a plane flying between New York and Madrid, which are both on the same line of latitude, does not fly along the line of latitude but instead has a path that looks curved when seen on a two-dimensional map.

Table of Contents

Introduction

CHAPTER ZERO

A Head for Numbers

CHAPTER ONE

The Counter Culture

CHAPTER TWO

Behold!

CHAPTER THREE

Something about Nothing

CHAPTER FOUR

Life of Pi

CHAPTER FIVE

The x-factor

CHAPTER SIX

Playtime

CHAPTER SEVEN

Secrets of Succession

CHAPTER EIGHT

Gold Finger

CHAPTER NINE

Chance is a Fine Thing

CHAPTER TEN

Situation Normal

CHAPTER ELEVEN

The End of the Line

GLOSSARY

APPENDICES

NOTES ON CHAPTERS

ACKNOWLEDGEMENTS

PICTURE CREDITS