The Magic of Mathematics: Discovering the Spell of Mathematics

344 Pages·1994·12.96 MB·English

by  Theoni Pappas

THE
MAGIC
OF
MATHEMATICS
Discovering the Spell of Mathematics
THEONI PAPPAS
author of The Mathematics Calendar &
The Joy of Mathematics
Copyright © 1994 by Theoni Pappas.
All rights reserved. No part of this work may be reproduced, copied or transmitted 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 a topic to not be
included.
Wide World Publishing/Tetra
P.O. Box 476
San Carlos, CA 94070
web sites:
http://www.wideworldpublishing.com
http://www.mathproductsplus.com
Ninth Printing, October 2011
Library of Congress Cataloging-in-Publication 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--dc20 94-11653
CIP
This book is dedicated to
mathematicians
who have created and
are creating
the magic of mathematics.
The moving power of mathematical invention is not reasoning but
imagination. —A. De Morgan • The essence of mathematics is its
freedom. —Georg Cantor • The beautiful has its place in mathematics
for here are the triumph of creative imagination. —W.K. White •
There is no branch of mathematics, however abstract, which may not
someday be applied to the phenomena of the real world. —Nikolai
Lobachevsky • It may well be doubted whether, in all the range of
science, there is any field so fascinating to the explorer — so rich in
hidden treasures — so fruitful in delightful surprises — as pure
mathematics. — Lewis Carroll • Mathematics rightly viewed possess
not only truth, but supreme beauty—a beauty cold and austere, like
that of a sculpture. —Bertrand Russell • As far as the laws of
mathematics refer to reality, they are not certain, and as far as they
are certain, they do not refer to reality. —Albert Einstein • The
profound study of nature is the most fertile source of mathematical
discoveries. —Joseph Fourier • Mathematics may be defined as the
subject in which we never know what we are talking about, nor
whether what we are saying is true,—Bertrand Russell • How can it
be that mathematics, a product of human thought independent of
experience, is so admirably adapted to the objects of reality. —Albert
Einstein • The mathematician does not study pure mathematics
because it is useful; he studies it because he delights in it and he
delights in it because it is beautiful. —Henri Poincaré
CONTENTS
PREFACE
MATHEMATICS IN EVERYDAY THINGS
MAGICAL MATHEMATICAL WORLDS
MATHEMATICS & ART
THE MAGIC OF NUMBERS
MATHEMATICAL MAGIC IN NATURE
MATHEMATICAL MAGIC FROM THE PAST
MATHEMATICS PLAYS ITS MUSIC
THE REVOLUTION OF COMPUTERS
MATHEMATICS & THE MYSTERIES OF LIFE
MATHEMATICS AND ARCHITECTURE
THE SPELL OF LOGIC, RECREATION & GAMES
SOLUTIONS
BIBLIOGRAPHY
INDEX
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 that 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 — worlds independent of ours — and presto these ideas
connect to our world almost as if a magic wand were 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.
Mathematics and sports are a dynamic duo. Baseball is full of math ideas from computing averages and
stats to the physics of pitching and batting.
Photo courtesy of the U.S. Federal Government.
MATHEMATICS IN EVERYDAY
THINGS
THE MATHEMATICS OF FLYING
THE MATHEMATICS OF A TELEPHONE CALL
PARABOLIC REFLECTORS & YOUR HEADLIGHTS
COMPLEXITY AND THE PRESENT
MATHEMATICS & THE CAMERA
RECYCLING THE NUMBERS
BICYCLES, POOL TABLES & ELLIPSES
THE RECYCLING NUMBERS
LOOKOUT FOR TESSELLATIONS
STAMPING OUT MATHEMATICS
MOUSE’S TALE
A MATHEMATICAL VISIT
THE EQUATION OF TIME
WHY ARE MANHOLES ROUND?