tailieunhanh - The Golden Ratio and Fibonacci Numbers

In this text, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Finobacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, latice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are. | The Golden Ratio and Fibonacci _The__n Golden Ratio and Fibonacci Numbers by Richard A. Dunlap Dalhousie University Canada World Scientific New Jersey London Singapore Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link Singapore 596224 USA office Suite 202 1060 Main Street River Edge NJ 07661 UK office 57 Shelton Street Covent Garden London WC2H 9HE Library of Congress Cataloging-ta-Publicatíon Data Dunlap R. A. The golden ratio and Fibonacci numbers R. A. Dunlap p- cm. Includes bibliographical references pp. 153-155 and index. ISBN 9810232640 alk. paper 1. Golden section. 2. Fibonacci numbers. I. Title. 1997 512 .72-dc21 97-28758 CIP British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. First published 1997 Reprinted 1998 1999 2003 Copyright 1997 by World Scientific Publishing Co. Pte. Ltd. Allrights reserved. This book or parts thereof may not be reproducedinanyformorby 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 .