The Magic Of Mathematics: Discovering The Spell Of Mathematics

THE IC MAG OF WA'-- - ! A- .. -gl -Z KmALL....-- Ill/ WIDE WORLD PUBLISHING/TETRA A...-- Copyright © 1994 by Theoni Pappas. All rights reserved. No part of this work may be reproduced or copied in any form or by any means without written permission from Wide World Publishing/Tetra. Portions of this book have appeared in previously published works, but were too essential to not be included. Wide World Publishing/Tetra P.O. Box 476 San Carlos, CA 94070 Printed in the United States of America. Second Printing,October 1994. Library of Congress Cataloglng-in-Publlcatlon Data Pappas, Theoni, The magic of mathematics: discovering the spell of mathematics / Theoni Pappas. P. cm. Includes bibliographical references and index, ISBN 0-933174-99-3 1. Mathematics- -Popular works. I. Title. QA93, P368 1994 510--dc2O 94-11653 CIP This book is dedicated to mathematicians who have created and are creating the magic of mathematics. CONTE NTS PREFACE I MATH EMATICS IN EVERYDAY THINGS 3 MAGICAL MATHEMATICAL WORLDS 33 MATHEMATICS &ART 63 THE MAGIC OF NUMBERS 97 MATHEMATICAL MAGIC IN NATURE 119 MATHEMATICAL MAGIC FROM THE PAST 143 MATHEMATICS PLAYS ITS MUSIC 173 THE REVOLUTION OF COMPUTERS 189 MATHEMATICS &THE MYSTERIES OF LIFE 223 MATHEMATICS AND ARCHITECTURE 243 THE SPELL OF LOGIC, RECREATION & GAMES 265 SOLUTIONS 311 BIBLIOGRAPHY 315 INDEX 321 TH EMAC IC O F MATH EMATICS 1 PREFACE You don't have to solve problems or be a mathematician to discover the magic of mathematics. This book is a collection of ideas - ideas with an underlying mathematical theme. It is not a textbook. Do not expect to become proficient in a topic or find an idea exhausted. The Magic of Mathematics delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Many think of mathematics as a rigid fixed curriculum. Nothing could be further from the truth. The human mind continually creates mathematical ideas and fascinating new worlds independent of our world - and presto these ideas connect to our world almost as if a magic wand had been waved. The way in which objects from one dimension can disappear into another, a new point can always be found between any two points, numbers operate, equations are solved, graphs produce pictures, infinity solves problems, formulas are generated - all seem to possess a magical quality. Mathematical ideas are figments of the imagination. Its ideas exist in alien worlds and its objects are produced by sheer logic and creativity. A perfect square or circle exists in a mathematical world, while our world has only representations of things mathematical. The topics and concepts which are mentioned in each chapter are by no means confined to that section. On the contrary, examples can easily cross over the arbitrary boundaries of chapters. Even if it were possible, it would be undesirable to restrict a mathematical idea to a specific area. Each topic is essentially self-contained, and can be enjoyed independently. I hope this book will be a stepping stone into mathematical worlds. -t rw \"' Print Gallery