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World Scientific
N E W J E R S E Y • L O N D O N • S I N G A P O R E • B E I J I N G • S H A N G H A I • H O N G K O N G • TA I P E I • C H E N N A I
Published by
World Scientific Publishing Co. Pte. Ltd.
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Library of Congress Cataloging-in-Publication Data
Stakhov, A. P. (Alexey Petrovich)
The mathematics of harmony : from Euclid to contemporary mathematics puter science / by Alexey
Stakhov ; assisted by Scott Olsen.
p. cm. -- (Series on knots and everything ; v. 22)
Includes bibliographical references and index.
ISBN-13: 978-981-277-582-5 (hardcover : alk. paper)
ISBN-10: 981-277-582-X (hardcover : alk. paper)
1. i numbers. 2. Golden section. 3. Mathematics--History. 4. Computer science. I. Olsen, Scott
Anthony II. Title.
2009
'2--dc22
2009021159
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2009 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or
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be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center,
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Printed in Singapore.
EH - The Mathematics 1 7/17/2009, 9:41 AM
Dedication
v
With deep gratitude to my parents, my darling father, Peter Stakhov,
who was killed in 1941 during World War II (19411945),
and to my darling mother, Daria Stakh, who passed