ENCYCLOPEDIA OF Mathematics and Society ENCYCLOPEDIA OF Mathematics and Society Sarah J. Greenwald Jill E. Thomley Appalachian State University VOLUME 1 Salem Press Copyright © 2012, by Salem Press All rights in this book are reserved. No part of this work may be used or reproduced in any manner whatsoever or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without written permission from the copyright owner except in the case of brief quotations embodied in critical articles and reviews or in the copying of images deemed to be freely licensed or in the public domain. For information, address the publisher, Salem Press, at [email protected]. The paper used in these volumes conforms to the American National Standard for Permanence of Paper for Printed Library Materials, X39.48-1992 (R1997). Library of Congress Cataloging-in-Publication Data Encyclopedia of mathematics and society / Sarah J. Greenwald , Jill E. Thomley, general Editors. p. cm. Includes bibliographical references and index. ISBN 978-1-58765-844-0 (set : alk. paper) -- ISBN 978-1-58765-845-7 (v. 1 : alk. paper) -- ISBN 978-1-58765-846-4 (v. 2 : alk. paper) -- ISBN 978-1-58765-847-1 (v. 3 : alk. paper) 1. Mathematics--Social aspects. I. Greenwald, Sarah J. II. Thomley, Jill E. QA10.7.E53 2012 303.48’3--dc23 2011021856 First Printing Printed in the United States of America Produced by Golson Media President and Editor J. Geoffrey Golson Senior Layout Editor Mary Jo Scibetta Author Manager Joseph K. Golson Copy Editors Carl Atwood, Kenneth Heller, Holli Fort Proofreader Lee A. Young Indexer J S Editorial Contents Volume 1 Publisher’s Note vi About the Editors viii Introduction ix List of Articles xiii Topic Finder xxi List of Contributors xxvii Articles A to E 1–376 Volume 2 List of Articles vii Articles F to O 377–744 Volume 3 List of Articles vii Articles P to Z 745–1089 Chronology 1091 Resource Guide 1109 Glossary 1113 Index 1127 Photo Credits 1191 Publisher’s Note The Encyclopedia of Mathematics and Society (three The articles in the set fall into one or more of the volumes) explains how mathematics is at the root of following broad categories: architecture and engi- modern civilization, from measuring temperature on neering (35 articles); arts, music, and entertainment a frigid day to driving a car to using a digital camera; (41): business, economics, and marketing (32); com- enthusiasts might say applied mathematics rules the munication and computers (22); friendship, romance, world. The set includes 478 articles, all of which were and religion (18); games, sport, and recreation (42); written specifically for the work. government, politics, and history (43); history and development of curricular concepts (63); mathemat- Scope of Coverage ics around the world (21); mathematics culture and The Encyclopedia of Mathematics and Society is designed identity (27); medicine and health (34); school and to provide students at the high school and under- society (19); space, time, and distance (25); travel and graduate levels with a convenient source of informa- transportation (18); and weather, nature, and envi- tion on the fundamental science and the mathematics ronment (35). behind our daily lives, explaining to students how and why mathematics works, and allowing readers to bet- Rationale for Choice of Topics ter understand how disciplines such as algebra, geom- Mathematics is a fundamental part of society, yet etry, calculus, and others affect what we do every day. many people may not be aware of the interconnections This academic, multiauthor reference work serves as between what they have learned in school and their a general and nontechnical resource for students and everyday lives. In its Curriculum Guide (MAA, 2004), teachers to understand the importance of mathemat- the Mathematical Association of America’s Committee ics; to appreciate the influence of mathematics on soci- on the Undergraduate Program in Mathematics eties around the world; to learn the history of applied (CUPM) recommends that mathematics programs mathematics; and to initiate educational discussion lead people “to learn mathematics in a way that helps brought forth by the specific social and topical articles them to better understand its place in society: its presented in the work. meaning, its history, and its uses.” In keeping with this vi philosophy, the editors chose topics for inclusion based their introduction to the encyclopedia. The “List of on one or more of the following criteria: Articles,” repeated in all three volumes, features all the articles in alphabetical order with page numbers as they • The topic is timely and likely to remain so. are listed in the encyclopedia. A “Topic Finder” shows • The topic can be tied to mathematical all the articles organized by category to enable readers concepts that people likely have been to find related article by topic. The “List of Contribu- exposed to. tors” presents all the writers for the encyclopedia along • The topic is related to concepts and with their academic or institutional affiliations. connections that professional mathematical The backmatter of the encyclopedia at the end of organizations have suggested are important. Volume 3 has the “Chronology of Mathematics,” a time- • The topic is one that the general public has line of major milestones in the discoveries and devel- expressed interest in. opment of mathematics. Next is the “Resource Guide” • The topic is one we have successfully used or for further research that includes books that are major that we know has been successfully used in works in the history of mathematics as well as current other contexts. editions of new works, journals in the mathematics field, and Internet sites that pertain to mathematics. Article Length and Format A “Glossary” provides mathematical definitions for Articles in the encyclopedia range in length from 500 terms encountered in the articles. Lastly, a comprehen- to 3500 words. Each is first presented with the cat- sive subject index references all concepts, terms, events, egory to which it belongs (for example, architecture persons, places, and other topics of discussion. and engineering), an article summary, and fields of study for the article. The fields of study include the Online Access following: Salem provides access to its award-winning content both in traditional printed form and online. 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Many • A simple, intuitive interface articles are richly illustrated with photos and captions, • User profile areas for students and patrons and charts, graphs, and tables. Finally, each article is • Sophisticated search functionality signed by the contributor to the encyclopedia. • Complete content, including appendixes • Integrated searches with any other Salem Frontmatter and Backmatter Press product you already have on the Salem Volume 1 of the Encyclopedia of Mathematics and Soci- Science platform ety begins with “About the Editors” and then presents • E-books are also available vii About the Editors Sarah J. Greenwald is a professor of mathematics and Jill E. Thomley is an associate professor of statistics a women’s studies core faculty member at Appala- in the Department of Mathematical Sciences at Appa- chian State University in Boone, North Carolina. She lachian State University. Her education and scholarly obtained her Ph.D. in mathematics from the University interests are diverse, generally focusing on mathematics of Pennsylvania in 1998 and since then has published and science applications. She earned a Ph.D. in Deci- more than 35 articles. Her areas of expertise include sion Sciences from Rensselaer Polytechnic Institute Riemannian geometry, popular culture as it pertains to and was awarded the Del and Ruth Karger Dissertation mathematics, and women and minorities in mathemat- Prize and a Rensselaer Founders Award of Excellence. ics. Dr. Greenwald has discussed the impacts of scien- Additional degrees include an M.S. in industrial/orga- tific popular culture representations on NPR’s Science nizational psychology from Rensselaer and an A.B. in Friday. She has spoken all over the country, and her psychology from Harvard University. interactive mathematics lecture appears on 20th Cen- Along with teaching, Dr. Thomley consults on sta- tury Fox’s Futurama movie Bender’s Big Score. tistical design and analysis of scientific research and Dr. Greenwald has won numerous teaching awards evaluates the results of federal education grants. Areas including a Mathematical Association of America Alder of focus include computational science, a discipline Award for Distinguished Teaching and an Appalachian arising from the intersection of science, mathematics, State University Wayne D. Duncan Award for Excellence and computer science, and the adoption and diffu- in Teaching in General Education. Dr. Greenwald has sion of educational innovations in mathematics and also been active in professional service as a member of science. She presented at the first Science in Society the Joint Policy Board for Mathematics Advisory Panel Conference in 2009 and was published in The Inter- for Mathematics Awareness Month and as the associate national Journal of Science in Society. Additional inter- editor for the Association for Women in Mathematics, ests include history of statistics and statistics in popu- just to name a few. Her husband, Joel Landsberg, is the lar culture. bassist for the Kruger Brothers. viii Introduction Mathematics is pervasive in modern society, and on passed their knowledge on to the next generation; the some level we all use mathematics in our daily lives. At fundamental connections to daily tasks of living; the the same time, many people are not fully aware of the ethics, controversies, and philosophies surrounding diverse interactions and connections between mathe- mathematics; the public’s perceptions of mathemat- matics and society. Mathematics takes a readily appar- ics and mathematicians; the way current society uses ent starring role in highly technological fields like engi- mathematics to solve problems and educate its citizens; neering, computer science, and the natural sciences. and the way mathematics draws from society in order Outside these fields, however, there are countless ideas, to grow and evolve. inventions, and advances that cannot be fully realized Mathematics shapes the world in which we live. In without the involvement of mathematics. the twenty-first century it is almost impossible to find Organizations like the National Council of Teachers an academic field of study that does not use mathemat- of Mathematics and the Mathematical Association of ics, either directly or via tools and technology in which America recommend that mathematics be explored in mathematics plays a vital role. The world in turn shapes the context of contemporary society. To examine these the discipline of mathematics by inspiring mathemati- connections, we approach them from different angles. cians to formulate new questions, solve new problems, We can look at mathematics through the lens of larger develop new theories, and use new technologies. Each societal structures like nations, cultures, and educa- successive generation of mathematicians brings fresh tional systems, or we can turn this method around to perspectives, expectations, and ways of thinking and explore the societal structures within mathematics, working into the culture of mathematics. These math- such as the culture of mathematicians and notions of ematicians are influenced by the home, school, and proof, certainty, and success. play environments in which they were raised. Connections are also found in the countless applica- However, despite the mathematics all around us, tions of mathematics to society. Overall, definitions and people’s exposure may be limited. Representations in applications of mathematics are inherently dependent the media or in popular culture may portray math- on context: the socio-historical events during which ematics and mathematicians in highly stereotypical they developed; the people who created or discovered ways that do not reflect the true depth, breadth, diver- concepts, who built upon the work of others, or who sity, and culture of the mathematics community. iixx