Figuring It Out Entertaining Encounters with Everyday Math
This is a book of mathematical stories — funny and puzzling mathematical stories. They tell of villains who try to steal secrets, heroes who encode their messages, and mathematicians who spend years on end searching for the best way to
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NUNO CRATO
FIGURING IT OUT ENTERTAINING ENCOUNTERS WITH EVERYDAY MATH
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Nuno Crato Universidade Técnica de Lisboa Inst. Superior de Economia e Gestão Dept. Matemática Rua Miguel Lupi 20 1200 Lisboa Portugal [email protected]
Original Portuguese edition published by Gradiva Publicações lda., Lisboa, Portugal, 2008 original title: A Matemática das Coisas ISBN 978-3-642-04832-6 e-ISBN 978-3-642-04833-3 DOI 10.1007/978-3-642-04833-3 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010930692 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, 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 protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
PREFACE
“When I tell people that I am a mathematician, they jokingly ask if I could help them balance their bank account. Then, when I tell them I make lots of counting mistakes, they think I must be a pretty mediocre mathematician.” That is what one mathematician friend of mine once told me, but it could as easily have come from just about any mathematician, as almost everyone in this field complains of how misunderstood the profession is. There really are a lot of people who have no idea what it is that mathematicians do. Math, of course, is an integral part of our daily lives. The 20th century could not have been the most revolutionary one hundred years in the history of science, as indeed it was, without the extraordinary advances that took place in the field of mathematics. Computers could not have been created without binary logic, group theory and the mathematical concept of information. Telephones would not work if mathematicians hadn’t developed the statistical study of signals and the algorithms to digitalize and compress data. Automated traffic lights would no doubt effect chaos, rather than order, if advances in a field of mathematics called Operations Research had not occurred. But despite its crucial importance, mathematics is frequently viewed as an insular, even irrelevant field into which few interesting people venture, and which has little to contribute to our daily lives. Even the well-educated often demonstrate a surprising ignorance of the history of mathematics and its
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