For our entire range of books please use search strings "Orient BlackSwan", "Universities Press India" and "Permanent Black" in store. Universities Press (India) Private Limited Registered Office 3-6-747/1/A & 3-6-754/1, Himayatnagar, Hyderabad 500 029 (A.P.), INDIA e-mail: [email protected] Distributed by Orient Blackswan Private Limited Registered Office 3-6-752 Himayatnagar, Hyderabad 500 029 (A.P.), INDIA e-mail: [email protected] Other Offices Bangalore, Bhopal, Bhubaneshwar, Chennai, Ernakulam, Guwahati, Hyderabad, Jaipur, Kolkata, Lucknow, Mumbai, New Delhi, Noida, Patna © Universities Press (India) Private Limited 2002 First published 2002 Reprinted 2010 eISBN 978-81-7371-969-1 e-edition:First Published 2015 ePUB Conversion: Techastra Solutions Pvt. Ltd. All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law. For permission requests write to the publisher. Contents Title Page Copyright Preface Acknowledgements 1 Multiplication 1.1 Early methods 1.2 Napier’s bones 1.3 Multiplication tables 1.4 Interlude on prime factorization 1.5 Parabolic multiplication 1.6 Interlude on nomograms 2 Indices 2.1 The laws of indices 2.2 Big numbers 2.3 The four twos 2.4 Negative exponents 2.5 Fractional exponents 2.6 Exponential notation in science 3 Geometric Series 3.1 The powers of 2 3.2 The powers of 3 3.3 Recurring decimals 3.4 Achilles and the tortoise 4 Logarithms 4.1 Definition 4.2 Genesis of the logarithm 4.3 Brief historical details 4.4 Estimation of logarithms 4.5 Logarithms to base 2 4.6 Common logarithms 5 Computation of Logarithms 5.1 Logarithms in binary form 5.2 Logarithms via square roots 5.3 Interpolation techniques 5.4 Interlude on interpolation 5.5 Using the exponential function 6 Compound Interest 6.1 Interest 6.2 Doubling your money 7 Sensational Stuff 7.1 Stimulus and sensation 7.2 ‘The Versatile Logarithm’–I 8 Measuring Sound 8.1 How do we hear sounds? 8.2 Qualities of sounds 8.3 The decibel scale 8.4 The musical scale 8.5 ‘The Versatile Logarithm’–II 9 Three Applications 9.1 Starry starry night 9.2 Earthquake! 9.2.1 Seismology 9.2.2 The Richter scale 9.2.3 Storm warning 9.3 Sweet and sour 10 The Number e 10.1 Genesis of e 10.2 A graphical approach 10.3 Explanations 10.4 Natural logarithms 11 The Mystique of e 11.1 Derangements 11.2 The nth root of n 11.3 Various series for e 11.4 Continued fractions for e 11.5 The factorial numbers 11.6 Prime numbers 11.7 π and e 11.7.1 Euler’s formula 11.7.2 The “bell curve” 11.7.3 An infinite series plus an infinite GCF 11.7.4 A gem from Ramanujan 11.8 A final comment 12 Miscellaneous Applications 12.1 Radioactivity 12.2 Population growth 12.3 Cooling down 12.4 Parachuting down 12.5 The hanging necklace 12.6 The logarithmic spiral 12.6.1 A brief note on polar coordinates 12.6.2 On spiral forms in nature 12.7 In conclusion 13 An Areal View 13.1 The function L(t) 13.2 Approximate values 13.3 Properties of L(t) 13.4 For which t is L(t) equal to 1? 13.5 Identification of L(t) A The Irrationality of e B An Infinite Series for e C Solutions Bibliography