m o c c. ntifi e ci s d orl w w. w w m o d fr e d a o nl w o D 1122881122__99778899881111225555446655__ttpp..iinndddd 11 88//77//2222 88::2266 AAMM Problem Solving in Mathematics and Beyond Print ISSN: 2591-7234 Online ISSN: 2591-7242 Series Editor: Dr. Alfred S. Posamentier Distinguished Lecturer New York City College of Technology - City University of New York There are countless applications that would be considered problem solving in mathematics and beyond. One could even argue that most of mathematics in one way or another involves solving problems. However, this series is intended to be of interest to the general audience with the sole purpose of demonstrating the power and beauty of mathematics through clever problem-solving experiences. Each of the books will be aimed at the general audience, which implies that the m o writing level will be such that it will not engulfed in technical language — rather c c. entifi tchoen ltaenngt uaangde n woitl lb bee d siismtrapclete edv ebryy duanyn elacnegssuaargiley s soo tphhaits tchaet efdo cluasn gcuanag ree.m Aagina ionn, tthhee ci ds primary purpose of this series is to approach the topic of mathematics problem- orl solving in a most appealing and attractive way in order to win more of the w w. general public to appreciate his most important subject rather than to fear it. At w w the same time we expect that professionals in the scientific community will also m o find these books attractive, as they will provide many entertaining surprises for the d fr unsuspecting reader. e d a o wnl Published o D Vol. 28 Seduced by Mathematics: The Enduring Fascination of Mathematics by James D Stein Vol. 27 Mathematics: Its Historical Aspects, Wonders and Beyond by Alfred S Posamentier and Arthur D Kramer Vol. 26 Creative Secondary School Mathematics: 125 Enrichment Units for Grades 7 to 12 by Alfred S Posamentier Vol. 25 Geometry in Our Three-Dimensional World by Alfred S Posamentier, Bernd Thaller, Christian Dorner, Robert Geretschläger, Guenter Maresch, Christian Spreitzer and David Stuhlpfarrer For the complete list of volumes in this series, please visit www.worldscientific.com/series/psmb BBaallaassuubbrraammaanniiaann -- 1122881122 -- SSeedduucceedd bbyy MMaatthheemmaattiiccss..iinndddd 11 2299//66//22002222 44::4466::2211 ppmm m o c c. ntifi e ci s d orl w w. w w m o d fr e d a o nl w o D 1122881122__99778899881111225555446655__ttpp..iinndddd 22 88//77//2222 88::2266 AAMM 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 Control Number: 2022017162 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. m o Problem Solving in Mathematics and Beyond — Vol. 28 c c. SEDUCED BY MATHEMATICS ntifi The Enduring Fascination of Mathematics e ci Copyright © 2023 by World Scientific Publishing Co. Pte. Ltd. s d orl All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, w w. electronic or mechanical, including photocopying, recording or any information storage and retrieval ww system now known or to be invented, without written permission from the publisher. m o d fr e d a o nl w For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance o D Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-125-546-5 (hardcover) ISBN 978-981-125-635-6 (paperback) ISBN 978-981-125-547-2 (ebook for institutions) ISBN 978-981-125-548-9 (ebook for individuals) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/12812#t=suppl Desk Editors: Balasubramanian Shanmugam/Rok Ting Tan Typeset by Stallion Press Email: [email protected] Printed in Singapore BBaallaassuubbrraammaanniiaann -- 1122881122 -- SSeedduucceedd bbyy MMaatthheemmaattiiccss..iinndddd 22 2299//66//22002222 44::4466::2211 ppmm 9”x6” b4628 Seduced by Mathematics Preface — Just What Does She See in Him, Anyway? m o c c. ntifi e ci s d orl Many of us know a bright, attractive woman with a good job and a lot w w. going for her … and a boyfriend who just doesn’t seem to be in the w w same league. It’s not that he’s an unshaven slob but he doesn’t seem m o to be the guy she deserves. And everyone has asked, “Just what does ed fr she see in him, anyway?” d a nlo “Just what do you see in math, anyway?” is a familiar question for w o everyone who likes, loves or teaches math — at least when they D encounter someone who doesn’t share their feelings. Of course, it’s not just math. If you are a jazz aficionado or an American who likes soccer, you’ve probably heard something similar. So what do you do? If you’re a jazz aficionado, you find the most universally appealing jazz you can find and play it for your friend. If you like soccer, you find videos of incredible goals. But what do you do if you are me, and feel the way I do about math? That’s easy. You write this book. This book would not have been written had I not encountered several people along the way who made critical contributions. First up is my wife, Linda. She and her mother visited Taiwan in early January 2020, and when she returned I contracted pneumonia. Despite my saying, “I’m sure it’s just a cold,” she made sure I got proper medical attention, including 6 weeks of caring for me when v bb44662288__FFMM..iinndddd 55 77//88//22002222 22::2244::4444 PPMM 9”x6” b4628 Seduced by Mathematics vi Seduced by Mathematics: The Enduring Fascination of Mathematics I literally couldn’t do anything. Covid was putting in an appearance at the time, and I’m pretty sure that had she not done what she did, I wouldn’t be here to write this book. Next are John Bachar and Ken Warner, two good friends and col- leagues from California State University, Long Beach. Mathematicians are grouped in families in much the same way as real people are. Ken’s thesis advisor at UCLA was Angus Taylor, who was also the thesis advisor for Bill Bade, who was my thesis advisor. John’s thesis advisor was Phil Curtis, who co-authored many brilliant and insightful papers with Bill. Bill talked Phil into hiring me at UCLA, and John and Ken were instrumental in seeing that I was hired at CSULB and that m I received tenure. I’m grateful to have this opportunity to express my o c c. appreciation for their support and friendship over the years. ntifi Oh, yes, without John and Ken, I would not be married to the e ci s aforementioned Linda — because I met her while she was a grad stu- d worl dent at CSULB. So, I owe them more than just a career. w. w And finally, there’s Al Posamentier, with whom I have had the w m pleasure of doing a number of delightful podcasts on his excellent o d fr books, and who has enabled me to have my last three books pub- e ad lished. Al and I have yet to meet in person, but I’m looking forward to o wnl the opportunity. o D My father used to say of someone, “He’s a gentleman and a scholar — and there are damned few of us left.” I know John and Ken fall into that category, and I’d bet large sums that Al does, too. bb44662288__FFMM..iinndddd 66 77//88//22002222 22::2244::4444 PPMM 9”x6” b4628 Seduced by Mathematics About the Author m James D. Stein o c c. ntifi is a retired Professor of Mathe- e sci matics from California State University (Long d orl Beach, California), where he taught from 1975 to w w. 2013. He graduated from Yale University with a w w m B.A. in Mathematics and a minor in Physics, and o d fr received a Ph.D. in Mathematics from the de University of California at Berkeley. He has pub- a o nl lished over 40 research papers, approximately w o D half in Banach spaces and algebras and half in fixed points, but has also published several papers in physics and mathematics education. He taught courses at both undergraduate and graduate levels but specialized in teaching courses in mathematics education and calculus, real analysis and functional analysis. He served as a Content Review Expert for the textbook adoption for the State of California in both 2000 and 2013. He is also the author of The Fate of Schrodinger's Cat approximately a dozen books on mathematics and science for the general public, including , published by World Scientific Publishing. In retirement, he does podcasts with authors of books on mathematics and science for New Books Network. vii bb44662288__FFMM..iinndddd 77 77//88//22002222 22::2244::4444 PPMM B1948 Governing Asia TTThhhiiisss pppaaagggeee iiinnnttteeennntttiiiooonnnaaallllllyyy llleeefffttt bbblllaaannnkkk m o c c. ntifi e ci s d orl w w. w w m o d fr e d a o nl w o D BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM 9”x6” b4628 Seduced by Mathematics Contents m Preface — Just What Does SheSee in Him, Anyway? o c c. ntifi About the Author v e ci s orld Introduction: Seduced by Mathematics vi1i w w. w Chapter 1 Seduced by Numbers 9 w m o Chapter 2 Seduced by Arithmetic 25 d fr e ad Chapter 3 Seduced by Patterns 47 o nl w o Chapter 4 Seduced by Analytic Geometry 67 D Chapter 5 Seduced by Mathematical Induction (and How to Avoid It) 85 Chapter 6 Seduced by Calculus I 99 Chapter 7 Seduced by Complex Numbers 113 Chapter 8 Seduced by Infinite Series 129 Chapter 9 Seduced by Probability 147 Chapter 10 Seduced by Infinity 163 ix bb44662288__FFMM..iinndddd 99 77//88//22002222 22::2244::4444 PPMM