Real-Life Math: Everyday Use of Mathematical Concepts

180 Pages·2002·1.8 MB·English

by  Evan M. Glazer

Real-Life Math

Real-Life Math
everyday use of
mathematical concepts
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▲ ▲
EVAN M. GLAZER and JOHN W. McCONNELL
An Oryx Book
GREENWOODPRESS
Westport,Connecticut • London
Library of Congress Cataloging-in-Publication Data
Glazer, Evan, 1971– .
Real-life math : everyday use of mathematical concepts / Evan M. Glazer and
John W. McConnell.
p. cm.
Includes bibliographical references.
ISBN 0-313-31998-7 (alk. paper)
1. Mathematics—Popular works. I. McConnell, John W. II. Title.
QA93 .G45 2002
510—dc21 2001058635
British Library Cataloguing in Publication Data is available.
Copyright ©2002 by Evan M. Glazer and John W. McConnell
All rights reserved. No portion of this book may be
reproduced, by any process or technique, without the
express written consent of the publisher.
Library of Congress Catalog Card Number: 2001058635
ISBN: 0-313-31998-7
First published in 2002
Greenwood Press, 88 Post Road West, Westport, CT06881
An imprint of Greenwood Publishing Group, Inc.
www.greenwood.com
Printed in the United States of America
The paper used in this book complies with the
Permanent Paper Standard issued by the National
Information Standards Organization (Z39.48-1984).
10 9 8 7 6 5 4 3 2 1
DEDICATED TO
the mathematics teachers at Glenbrook South High School
who were fearless in adapting real-world applications
to their lessons, and who generously shared
their best teaching ideas with us

Contents
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Introduction, ix
MATHEMATICALCONCEPTS
Angle, 1
Asymptote, 7
Cartesian Coordinates, 10
Circles, 12
Circumference, 16
Complex Numbers, 16
Conic Sections, 18
Counting, 21
Derivative, 23
Equations, 23
Expected Value, 26
Exponential Decay, 28
Exponential Growth, 30
Fibonacci Sequence, 35
Imaginary Numbers, 37
Integration, 37
Inverse (Multiplicative), 43
Inverse Function, 45
Inverse Square Function, 47
viii CONTENTS
Linear Functions, 49
Logarithms, 55
Logistic Functions, 58
Matrices, 61
Perimeter, 64
Periodic Functions, 67
Plane, 70
Polar Coordinates, 72
Polynomial Functions, 75
Probability, 77
Proportions, 82
Pythagorean Theorem, 87
Quadratic Functions, 89
Quadrilaterals, 93
Rates, 96
Ratio, 102
Reflections, 107
Rotations, 111
Sequences, 114
Series, 117
Similarity, 121
Slope, 124
Square Roots, 124
Standard Deviation, 127
Step Functions, 130
Surface Area, 133
Symbolic Logic, 136
Symmetry, 138
Tangent, 141
Translations, 144
Triangle Trigonometry, 146
Variation, 150
Vectors, 154
Volume, 159
Bibliography, 163
Introduction
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“When are we ever going to use this?”
This plaintive question from frustrated mathematics students is heard in schools
around our country as they wrestle with pages of abstract mathematics and learn
algorithms that appear to go nowhere. They study real numbers, but don’t find
any reason to believe that they are real. Thousands of American students still
work from textbooks that limit applications to age problems and mixtures of
nuts. Despite the call from the National Council of Teachers of Mathematics in
the Principles and Standards for School Mathematics (2000) for meaningful
learning through study of realistic applications, many students will find that the
only modernization of content over their grandparents’ math books is that jet
planes have replaced the trains that used to travel at different rates between cities.
The twentieth century saw an explosion of applications of mathematics. It is
now hard to find a field of study that does notuse mathematical tools. Biologists
use differential equations. Chemists use solid geometry to describe molecules.
Set designers in theaters use trigonometry to determine the best lighting for a
play. Historians determine authorship of obscure documents through statistical
analysis of words. Governments, international corporations, and individual in-
vestors use mathematical rules to determine production, employment, and prices.
Everybody uses computers. Unfortunately, even good students don’t know how
mathematics affects their lives. Few understand the power of compound interest.
Few realize that the compound interest embedded in credit cards can bring adults
to bankruptcy. Few know the mathematical implications of public policies that
will affect their lives. Even fewer know how to make best decisions based on the
probabilities of risk rather than blind gambles.
The secondary-school mathematics curriculum is faced with multiple chal-
lenges. What should students know and be able to do? Proficiency in some algo-
rithms is important. Abstraction in mathematics—stripping concepts of all but