E-Book Overview
This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has its origins in "The Elements" of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the "golden" algebraic equations, the generalized Binet formulas, Fibonacci and "golden" matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and "golden" matrices).The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
E-Book Content
This page intentionally left blank World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TA I P E I • CHENNAI 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 Cataloging-in-Publication Data Stakhov, A. P. (Alexey Petrovich) The mathematics of harmony : from Euclid to contemporary mathematics and computer 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. Fibonacci numbers. 2. Golden section. 3. Mathematics--History. 4. Computer science. I. Olsen, Scott Anthony II. Title. QA246.5.S73 2009 512.7'2--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 mechanical, including photocopying, recording or any information storage and retrieval system now known or to 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, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Printed in Singapore. EH - The Mathematics Harmony.pmd 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 (1941 1945), and to my darling mother, Daria Stakh, who passed away in 2001, and to my darling teacher Professor Alexander Volkov, who passed away in 2007. This page intentionally left blank Preface vii Preface Academician Mitropolsky’s commentary on the scientific research of Ukrainian scientist Professor Alexey Stakhov, Doctor of Engineering Sciences I have followed the scientific career of Professor Stakhov for a long time— seemingly since the publication of his firs