Editorial Board David Bressoud Carl Pomerance Robert Devaney, Chair Hung-Hsi Wu 2000 Mathematics Subject Classification. Primary 49-01, 49-04, 49Q05, 53-01, 53-04, 53A10. Maple is a registered trade mark of Waterloo Maple, Inc., Ontario, Canad a The figure on the cover was created by the author, using Maple. Library of Congress Cataloging-in-Publication Data Oprea, John. The mathematics of soap films : explorations with Maple® / John Oprea. p. cm. (Student mathematical library, ISSN 1520-9121 v. 10) Includes bibliographical references and index. ISBN 0-8218-2118-0 (softcover : alk. paper) 1. Minimal surfaces—Data processing. 2. Soap bubbles. 3. Surface tension. 4. Maple (Computer file) I. Title. II. Series. QA644.067 2000 516.3'62—dc21 00-041614 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Assistant to the Publisher, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to reprint-permissionQams.org. © 2000 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 05 04 03 02 01 00
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