The Story of Numbers PDF
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The Story of Numbers 10516_9789813222922_TP.indd 1 30/6/17 2:01 PM IIScPress-WSPC Publication Print ISSN: 2529-7864 Online ISSN: 2529-7872 Series Editor: Amaresh Chakrabarti (Indian Institute of Science, India) Published: Vol. 1: Remembering Sir J C Bose by D P Sen Gupta, M H Engineer & V A Shepherd Vol. 2: Climbing the Limitless Ladder: A Life in Chemistry by C N R Rao Vol. 3: The Story of Numbers by Asok Kumar Mallik Vishnu Mohan - 10516 - The Story of Numbers.indd 1 13-07-17 5:18:52 PM IIIISSccPPrreessss--WWSSPPCC PPuubblliiccaattiioonn TThhee SSttoorryy ooofff NNNuuummmbbbeeerrrsss AAssookk KKuummaarr MMaalllliikk IInnddiiaann IInnssttiittuuttee ooff EEnnggiinneeeerriinngg SScciieennccee aanndd TTeecchhnnoollooggyy,, SShhiibbppuurr,, IInnddiiaa World Scientifi c NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO 111111111111111111111111111111000000000000000000000000000000555555555555555555555555555555111111111111111111111111111111666666666666666666666666666666______________________________999999999999999999999999999999777777777777777777777777777777888888888888888888888888888888999999999999999999999999999999888888888888888888888888888888111111111111111111111111111111333333333333333333333333333333222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222999999999999999999999999999999222222222222222222222222222222222222222222222222222222222222______________________________TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP..............................iiiiiiiiiiiiiiiiiiiiiiiiiiiiiinnnnnnnnnnnnnnnnnnnnnnnnnnnnnndddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd 222222222222222222222222222222 3333333333333300000000000000//////////////66666666666666//////////////1111111111111177777777777777 22222222222222::::::::::::::0000000000000011111111111111 PPPPPPPPPPPPPPMMMMMMMMMMMMMM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Names: Mallik, A. K. (Asok Kumar), 1947– Title: The story of numbers / by Asok Kumar Mallik (Indian Institute of Engineering Science and Technology, India). Description: New Jersey : World Scientific, 2017. | Series: IIScPress-WSPC publication ; vol 3 | Includes bibliographical references. Identifiers: LCCN 2017013738 | ISBN 9789813222922 (hc : alk. paper) Subjects: LCSH: Numeration--History. | Mathematics--History | Mathematics--Philosophy. Classification: LCC QA141.2 .M35 2017 | DDC 513.509--dc23 LC record available at https://lccn.loc.gov/2017013738 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2018 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Desk Editors: V. Vishnu Mohan/Kwong Lai Fun Typeset by Stallion Press Email: [email protected] Printed in Singapore Vishnu Mohan - 10516 - The Story of Numbers.indd 2 27-06-17 3:25:22 PM June30,2017 12:35 TheStoryofNumbers-9inx6in b2870-fm pagev To the loving memory of my wife Kaberi v b2530 International Strategic Relations and China’s National Security: World at the Crossroads TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk b2530_FM.indd 6 01-Sep-16 11:03:06 AM June30,2017 12:35 TheStoryofNumbers-9inx6in b2870-fm pagevii Preface This is not a textbook of mathematics, neither written by a mathematician nor written for mathematicians. There is a classical text entitled “Numbers”, which was originally written in German and subsequently translated into English. Both versions were published by Springer in the series on Graduate Texts in Mathematics. In the preface of the English edition, it has been mentioned that “this is not a book for the faint-hearted”. The present book is mainly aimed at those “faint-hearted” people who may otherwise have some interest in mathematics as non-professionals. I and, of course, the publisher think that there are enough people in this category so that a book at this level is desired. The present book can be followed with the knowledge of high-school level mathematics and is thus suitable for school students as well. An attempt has been made to arrange some basic facts on various kinds of numbers that mathematicians have found over a periodofafewmillennia.Mathematicsdemandsrigoroustreatments but here the emphasis is more on stories and anecdotes rather than rigour. The beauty of surprising connections between various numbers originating in different contexts, curious properties and patterns exhibited by innocuous numbers, how some new kinds of numbers have been created — all these are discussed more in the form of a story rather than hardcore mathematics. vii June30,2017 12:35 TheStoryofNumbers-9inx6in b2870-fm pageviii viii Preface Mathematics normally is not perceived as a popular subject. Therefore, I do not dare to say that this is targeted as a popular book on mathematics. Popular books on mathematics may be more unpopular.However,Ihaveincludedalonglistofexcellentreferences which are mostly in the category of so-called popular books, rather than textbooks, on mathematics. The reader may consult these references to dig deeper into any specific topic of his/her choice. Anotherveryrichsourceofinterestinginformationon“Numbers”are thesetofvideolecturesintheseries“Numberphile”,freelyavailable over the Internet in youtube. A few references are also mentioned as footnotes. These are the sources of the specific information under discussion at that location and are not meant for further reading. Many friends have helped me to complete this book. Special mention must be made of Professors Raminder Singh, Aparna (Dey) Ghosh, Pradipta Bandyopadhyay, Anindya Chatterjee and G. K. Ananthsuresh, all of whom read different versions of the manuscript and suggested a lot of corrections and improvements. For the mistakes that still remain, only I am responsible. My young friends Amit, Suhas and Rajarshi always encouraged me with their frank assessmentsofthecontentsandthequalityofwriting.Amitespecially helped me by supplying a lot of suitable material and providing me a tutorial on p-adic numbers, which I have finally included on his insistence. Finally I thank Professor Goutam Bandyopadhyay for allowing me to use his notes on hyperreal numbers. I express my sinceregratitudetoallthesepeople.Hopesomenon-mathematician adults and school children enjoy reading the book. June30,2017 12:35 TheStoryofNumbers-9inx6in b2870-fm pageix About the Author Asok Kumar Mallik is Honorary Dis- tinguished Professor at Indian Institute of Engineering Science and Technology, Shibpur. During 1971–2009 he was in the Faculty of Mechanical Engineering at Indian Institute of Technology, Kanpur. He was a Commonwealth Scholar at The Insti- tute of Sound and Vibration Research at Southampton, England and an Alexander von Humboldt Fellow at TH, Aachen and TU, Darmstadt in Germany. He has been electedaFellowofTheIndianNationalAcademyofEngineeringand all the three Science Academies of India. He has authored one book and several articles on high school mathematics. ix
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