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THE JOY OF MA THEM TICS DiscoveringMathematics All Around You
ni pappas
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nature * science * architecture * art
history * literature
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philosophy * music
Wide World Publishing/Tetra
Copyright i 1986, 1987, 1989 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. Revised Edition 1989 1st Printing 1986 2nd Printing 1987 3rd Printing May 1989 4th Printing September 1989 5th Printing March 1990 6th Printing September 1990 7th Printing May 1991 8th Printing September 1991 9th Printing December 1991 10th Printing July 1992 11th Printing April 1993 12th Printing December 1993 13th Printing October 1994 Wide World Publishing/Tetra P.O. Box 476 San Carlos, CA 94070
Printedin The United States of America ISBN: 0-933174-65-9 Library of Congress Cataloging-in-Publication Data Pappas, Theoni. The Joy of Mathematics / by Theoni Pappas. --Rev. ed. p. cm. Includes index. ISBN: 0-933174-65-9: $10.95 1. Mathematics -- Popular works. 1. Title. QA93. P365 1989 510 -- dc2O 89-16503 CIP
I hope this book will serve as an introductionto some of the many diversified facets of mathematics, and that the reader will be encouraged to explore in greater depth the ideas presented. -
Theoni Pappas
". .the universe stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the languageand interpret the charactersin which it is written. It is written in the language of mathematics,and its charactersare triangles,circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wanderingabout in a dark labyrinth." -Galileo
INTRODUCTION The Joy Of Mathematics and More Joy of Mathematics unveil concepts, ideas, questions, history, problems, and pastimes which reveal the influence and nature of mathematics. To experience the joy of mathematics is to realize mathematics is not some isolated subject that has little relationship to the things around us other than to frustrate us with unbalanced check books and complicated computations. Few grasp the true nature of mathematics - so entwined in our environment and in our lives. So many things around us can be described by mathematics. Mathematical concepts are even inherent in the structure of living cells. These books seek to help you become aware of the inseparable relationship of mathematics and the world by presenting glimpses and images of mathematics in the many facets of our lives. The joy of mathematics is similar to the experience of discovering something for the first time. It is an almost child-like feeling of wonder. Once you have experienced it you will not forget that feeling - it can be as exciting as looking into a microscope for the first time and seeing things that have always been around you that you have been unable to see before. When deciding how to organize The Joy Of Mathematics, at first certain divisions immediately came to mind-for example, mathematics and nature, mathematics and science, mathematics and art, and so forth. But mathematics and its relationship to our surroundings does not come already packaged into categories. Rather, mathematics and its occurrences are spontaneous with elements of surprise. Thus, the topics are randomly arranged to retain the true essence of discovery. The Joy Of Mathematics and
More Joy of Mathematics are designed to be opened at any point. Each section, regardless of how large or small, is essentially self-contained. After one experiences the sheer joy of mathematics, the appreciation of mathematics follows and then the desire to learn