"Counting'' by Benjamin Wardhaugh

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writing

counting before 31–62, 33, 41, 45, 48

number symbols and see number symbols

number words see number words

origins of 69–98, 75, 89, 93, 272

written calculation, first 82

Xagiopai, Amazonia 279–85

year, counting days and weeks in 112–17, 113

yojana (Sanskrit astronomy unit of distance in the region of twelve kilometres) 138–9

YouTube 220–1, 223, 252

Yucatan Peninsula 271–2

Yup’ik counting games 255–62, 255, 263, 269

zero

Arabic 158, 165, 168

Chinese 191

counting board 158–9

gestures for 55

Latin 158

Mayan 274–5, 276

Sanskrit 143, 158

Acknowledgements

I am grateful to the late Felicity Bryan, whose interest and enthusiasm helped to shape this project in its earliest stages. My current agent Carrie Plitt provided valuable help during the later stages of work on it.

My thanks to Arabella Pike and her team at William Collins, including Sam Harding and Alex Gingell.

Christopher Hollings read the book in draft, as did my parents Moira and Tony Wardhaugh; their comments and suggestions were of great value.

As always my greatest debt is to my wife Jessica and our three sons, whose support, advice and practical assistance at all stages of this project were invaluable.

About the Author

BENJAMIN WARDHAUGH is a historian and author, based in Oxford, UK. He holds degrees in mathematics, music and history, and was a fellow of All Souls College for twelve years. He researches and writes about mathematics in the past, and is the author of Gunpowder and Geometry and Encounters with Euclid.