Strength in Numbers

Sherman K. Stein

Description

An Easygoing, Highly Entertaining Refresher on all the Math You'll Ever Need.

What do two goats and a car have to do with making good decisions? Was the golden ratio used to build the Great Pyramid of Khufu? Can it be that some numbers are unmistakably "hot," while others are inherently "cool"? With his infectiously enthusiastic and engaging style, award-winning teacher and author Sherman K. Stein offers a new appreciation for mathematics, from the beauty of its logic ("as inevitable and memorable as a Mozart symphony") to its amazing power and pervasiveness in our lives. Requiring no math knowledge beyond basic arithmetic and high school geometry, Strength in Numbers is an enlightening introduction to all the math you'll ever need.
Partial table of contents:

ABOUT MATHEMATICS.

The Many Faces of Mathematics.

The Spell of Cool Numbers.

Don't Do a Number on Me.

It Ain't Necessarily So.

The Mother of Invention.

Some Proposals, Modest and Immodest.

FROM HIGH SCHOOL TO KINDERGARTEN.

You Will Never See a Large Number.

Five Things You Can Do with Two Numbers.

Out of Thin Air.

The Three Sides of a Right Triangle.

Turning an Eguation into a Picture.

Why Negative Times Negative Is Positive.

CLOSER AND CLOSER.

Zero over Zero.

Trying to Find a Curved Area.

Finding a Curved Area.

One Thought in Parting.

Further Reading.

Glossary of Symbols.

References.

Index.

Sujets

• Sciences et techniques
• Mathematics

Informations

• Publié par: Turner Publishing Company
• Date de parution: 02 mai 2008
• Nombre de lectures: 0
• EAN13: 9780470348840
• Langue: English

Extrait

Strength in Numbers
Strength in Numbers
Discovering the Joy and Power of Mathematics in Everyday Life
Sherman K. Stein

John Wiley Sons. Inc.
New York Chichester Weinheim Brisbane Singapore Toronto
This book is printed on acid-free paper.
Copyright 1996 by Sherman K. Stein. All rights reserved.
Published by John Wiley Sons, Inc.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone]. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, [phone], fax [phone], e-mail: [e-mail].
This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought.
Library of Congress Cataloging-in-Publication Data:
Stein, Sherman K.
Strength in numbers: discovering the joy and power of mathematics in everyday life / Sherman K. Stein.
p. cm.
Includes bibliographical references (p. - ) and index.
ISBN 0-471-32974-6 (paper : alk. paper)
1. Mathematics-Popular works. I. Title.
QA93.S684 1996
510-dc20
95-48056
10 9 8 7 6 5 4 3 2 1
You and I-all of us-can explore the inner and outer worlds far more than we imagine possible. Many of us close the doors too soon. I dedicate this book to all who are willing to open closed doors and open even wider the doors already open.
CONTENTS
Acknowledgments
Guide to Chapter Order
PART ONE About Mathematics
1. The Many Faces of Mathematics
Touching the elephant . . . A fresh look at mathematics . . . Conrad Hilton s view . . . John Adams s view
2. The Spell of Cool Numbers
The number 13 . . . The 4-minute mile . . . Missiles and numbers ending in 0s . . . The Gulf War
3. Hot Numbers
A subway system gets built . . . Numbers and experts . . . How to protect yourself
4. Don t Do a Number on Me
One word does not mean one number . . . Height and weight . . . Strawberries and intelligence . . . Incomes
5. Anecdote versus Number
Two ways of thinking . . . A study of psychics . . . A test of astrology . . . Murders . . . Drunk driving
6. It Ain t Necessarily So
A gene for talent . . . Nothing new . . . Over the hill at 30 . . . The Egyptian rope . . . Art and the golden ratio . . . Archimedes bath and lever . . . The last night of Galois . . . Gauss s triangle . . . Einstein s arithmetic . . . No Nobel Prize
7. The Rapid Idiots
What computers can do . . . and can t
8. The Mother of Invention
How the pure becomes the applied . . . Knots . . . Seeing inside a fruitcake . . . Secret codes
9. What Is a Job, Really?
The two parts . . . Like water
10. What s in It for Me?
All the occupations . . . How many in each . . . What mathematics each job needs
11. The Action Syndrome
From half a mind or two minds to one mind
12. Where Have All the Reforms Gone?
The long battle between basics and concepts . . . A look at mathematics reforms in the past . . . The latest reform
13. Some Proposals, Modest and Immodest
Suggestions to cartoonists, parents, pupils, businesses, mathematics departments, schools . . . Accept the split personality
PART TWO From High School to Kindergarten
14. How to Read Mathematics
Mathematics is a verb . . . Techniques for reading . . . Slow down
15. You Will Never See a Large Number
A reporter calls . . . Two games . . . But they are not just games
16. The Car and Two Goats
A famous puzzle . . . The embarrassed mathematicians . . . A do-it-yourself kit
17. Five Things You Can Do with Two Numbers
A fresh look at addition, subtraction, multiplication, and division . . . Exponents
18. Some Sum
An endless sum . . . Is it finite or infinite? . . . A geometric approach . . . An arithmetic approach
19. Out of Thin Air
An endless sum and the magic of banking
20. All There Is to Know about Fractions
A self-contained expos of the world of fractions . . . Why to divide, turn the denominator upside down and multiply
21. Is Every Number a fraction?
Rockets and the square root of 2 . . . How the Greeks viewed fractions . . . Surprise
22. The Three Sides of a Right Triangle
Geoboards . . . One picture is worth a thousand words
23. Pi Is a Piece of Cake-or Is It?
I try to teach pi . . . How to calculate it
24. Turning an Equation into a Picture
From letters to curves
25. Why Negative Times Negative Is Positive
Mathematicians simplify . . . Three explanations . . . The physicists are happy
26. A Fresh Look at Kindergarten
Drawing little sets . . . The infinite . . . What happened in 1873
PART THREE Closer and Closer
27. Zero over Zero
A Socratic dialog . . . The moral
28. How Steep Is a Curve?
The slope of a line . . . But the slope of a curve?
29. Trying to find a Curved Area
Rectangles are easy . . . But a curved area? . . . Frustration
30. Finding a Curved Area
A different approach . . . Success
31. The Circle and All the Odd Numbers
An argument from India
32. One Thought in Parting
Truth and beauty
Further Reading
Glossary of Symbols
References
Index
ACKNOWLEDGMENTS
As the manuscript of this book went through several revisions, it benefited from the comments of a wide variety of critics: professors of mathematics, laypersons, and junior high and high school students. It is a pleasure to acknowledge their assistance in making this exposition accessible to a broad audience.
Chris Garrett s beginning algebra class at Emerson Junior High School in Davis, California, and Joanne Moldenhauer s analysis class at Davis Senior High School commented on the mathematics chapters as extra credit assignments. I was impressed by the students insights and the clarity with which they expressed them.
Pat King and Heather Wade, mathematics teachers at Holmes Junior High School in Davis, offered several suggestions concerning the mathematics chapters and the chapters on jobs and reform.
Don Chakerian, professor of mathematics at the University of California at Davis, Sanford Siegel, professor of mathematics at the University of Rochester, and Lester Lange, professor of mathematics at California State University at San Jose, read the entire manuscript and caught several slips (even the introduction of a new false myth). Don Albers, head of publications at the Mathematical Association of America, Henry Alder, professor of mathematics at the University of California at Davis, Anthony Barcellos, professor of mathematics at American River College, and Anthony Wexler, professor of mechanical engineering at the University of Delaware, severe critics all, forced me to strengthen my case in the more polemical chapters. Sharon Dugdale, professor of mathematics education at the University of California at Davis, and Elaine Kasimatis, professor of mathematics at California State University at Sacramento, substantially improved the two chapters on reforms.
My wife, Hannah Stein, was the first person to read each chapter, often in its pen-and-ink stage. Her many suggestions helped clarify and humanize the exposition, for she insisted that the book not read like a mathematics text. No words can adequately acknowledge her contribution to this book any more than they can to my life.
Since I wanted the book to be accessible to readers who might have been away from mathematics a long time, or might not have used much mathematics in their careers, I also asked my friends, neighbors, relatives, and children to read various chapters. Their comments, which forced me to work much harder and longer than I had planned, made me meet my readers not halfway, but all the way. These critics-Ted Gould, Paul Jacobs, Dan Keller, Jane Keller, Don Kunitz, Allegra Silberstein, Lori Snyder, Joshua Stein, and Susanna Stein-came from such varied careers as library work, elementary through university teaching, journalism, law, marine biology, and public policy.
The reference librarians at the University of California at Davis made the millions of books and thousands of periodicals in its library as accessible as the books on my living room shelves. My thanks go to Rafaela Castro, Patsy Inouye, Linda Kennedy, Jane Kimball, Sandra Lamprecht, David Lundquist, Marcia Meister, Opritsa Popa, Juri Stratford, and Michael Winter.
I also wish to express my appreciation to my friend Roland Hoermann, professor of German, who translated Moritz Cantor s discussion of the possible use of the 3-4-5 right triangle by the Egyptians.
Anthony Barcellos created the illustrations, for which I am deeply appreciative.
I hope that anyone who has suggestions for improving the book will send them to me at the Mathematics Department, University of California at Davis, Davis, CA 95616-8633. (e-mail: [e-mail])
GUIDE TO CHAPTER ORDER
Part I can be read in any order, though Chapters 2 and 3 form a natural unit, as do Chapters 9 and 10, and Chapters 11, 12, and 13 .
In Part 2, Chapter 14, which advises how to read the language of mathematics, is central. Chapters 18 and 19 form a unit, and part of Chapter 25 uses Chapters 17 and 24 .
In Part 3, Chapters 27 through 31 should be read in order after Chapters 18 and 24 . Chapter 32 depends mainly on Chapter 18 .
PART ONE

About Mathematics
1
The Many Faces of Mathematics
Practically everyone can und