Higgins P. - Number Story - From Counting to Cryptography (Copernicus, 2008).pdf

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Number Story
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Number Story
From Counting to Cryptography
PETER M. HIGGINS
COPERNICUS BOOKS
An Imprint of Springer Science+Business Media
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Peter M. Higgins, BA, BSc, PhD
Department of Mathematical Sciences, University of Essex
Wivenhoe Park, Colchester, UK
Published in the United States by Copernicus Books,
An imprint of Springer Science+Business Media, LLC
Mathematics Subject Classification (2000): 11-01
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Control Number: 2007936363
ISBN 978-1-84800-000-1
e-ISBN 978-1-84800-001-8
Printed on acid-free paper.
© Springer-Verlag London Limited 2008
Apart from any fair dealing for the purposes of research or private study, or criticism
or review, as permitted under the Copyright, Designs and Patents Act 1988, this
publication may only be reproduced, stored or transmitted, in any form or by
any means, with the prior permission in writing of the publishers, or in the case
of reprographic reproduction in accordance with the terms of licences issued by
the Copyright Licensing Agency. Enquiries concerning reproduction outside those
terms should be sent to the publishers.
The use of registered names, trademarks, etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from the
relevant laws and regulations and therefore free for general use.
The publisher makes no representation, express or implied, with regard to the
accuracy of the information contained in this book and cannot accept any legal
responsibility or liability for any errors or omissions that may be made.
987654321
Springer Science+Business Media
springer.com
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Preface
ix
chapter 1
The First Numbers
1
How Should We Think About Numbers?
5
The Structure of Numbers
8
chapter
2
Discovering Numbers
17
Counting and Its Consequences
23
chapter
3
Some Number Tricks
31
What Was the Domino?
34
Casting Out Nines
35
Divisibility Tests
39
Magical Arrays
49
Other Magic Number Arrays
57
chapter
4
Some Tricky Numbers
61
Catalan Numbers
65
Fibonacci Numbers
67
Stirling and Bell Numbers
72
Hailstone Numbers
75
The Primes
77
Lucky Numbers
84
chapter 5
Some Useful Numbers
85
Percentages, Ratios, and Odds
85
Scientific Notation
88
Meaning of Means
90
v
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