The handy math answer book

522 Pages·2006·10.77 MB·English

by  Patricia L Barnes-Svarney

About the Authors
Thanks to science backgrounds and their numerous science publications, both
Patricia Barnes-Svarney and Thomas E. Svarney have had much more than a passing
acquaintance with mathematics.
Barnes-Svarney has been a nonfiction science and science-fiction writer for 20
years. She has a bachelor’s degree in geology and a master’s degree in geography/
geomorphology, and at one time she was planning to be a math major. Barnes-
Svarney has had some 350 articles published in magazines and journals and is the
author or coauthor of more than 30 books, including the award-winning New York
Public Library Science Desk Referenceand Asteroid: Earth Destroyer or New
Frontier?,as well as several international best-selling children’s books. In her spare
time, she gets as much produce and herbs as she can out of her extensive gardens
before the wildlife takes over.
Thomas E. Svarney brings extensive scientific training and experience, a love of
nature, and creative artistry to his various projects. With Barnes-Svarney, he has
written extensively about the natural world, including paleontology (The Handy
Dinosaur Answer Book), oceanography (The Handy Ocean Answer Book), weather
(Skies of Fury: Weather Weirdness around the World), natural hazards (A Paranoid’s
Ultimate Survival Guide), and reference (The Oryx Guide to Natural History). His
passions include martial arts, Zen, Felis catus,and nature.
When they aren’t traveling, the authors reside in the Finger Lakes region of
upstate New York with their cats, Fluffernutter, Worf, and Pabu.
The Handy Answer Book Series®
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(and Parents)
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The Handy Bug Answer Book
The Handy Dinosaur Answer Book
The Handy Geography Answer Book
The Handy Geology Answer Book
The Handy History Answer Book
The Handy Math Answer Book
The Handy Ocean Answer Book
The Handy Physics Answer Book
The Handy Politics Answer Book
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The Handy Religion Answer Book
The Handy Science Answer Book
The Handy Space Answer Book
The Handy Sports Answer Book
The Handy Weather Answer Book
Please visit us at www.visibleink.com.
THE
HANDY
MATH
ANSWER
BOOK

THE
HANDY
A N S W E R
BOOK
Patricia Barnes-Svarney and Thomas E. Svarney
Detroit
THE Copyright © 2006 by Visible Ink Press®
This publication is a creative work fully protected by all applicable copyright laws,
HANDY
as well as by misappropriation, trade secret, unfair competition, and other appli-
cable laws.
MATH No part of this book may be reproduced in any form without permission in writ-
ing from the publisher, except by a reviewer who wishes to quote brief passages
in connection with a review written for inclusion in a magazine or newspaper.
ANSWER
All rights to this publication will be vigorously defended.
BOOK Visible Ink Press®
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Line Art: Kevin Hile
Typesetting: The Graphix Group
ISBN 1-57859-171-6
Cover images of euros used by permission of Photographer's Choice/Getty Images;
Aristotle used by permission of The Bridgeman Art Library/Getty Images; woman
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Printed in the United States of America
All rights reserved
10 9 8 7 6 5 4 3 2 1
Contents
INTRODUCTION xi
ACKNOWLEDGMENTS xiii
H
ISTORY
HISTORY OF MATHEMATICS … 3
What Is Mathematics? . . . Early Counting and Numbers . . .
Mesopotamian Numbers and Mathematics . . . Egyptian Numbers
and Mathematics . . . Greek and Roman Mathematics . . . Other
Cultures and Early Mathematics . . . Mathematics after the Middle
Ages . . . Modern Mathematics
MATHEMATICS THROUGHOUT
HISTORY … 37
The Creation of Zero and Pi. . . Development of Weights
and Measures. . .Time and Math in History. . .
Math and Calendars in History
vii
T B
HE ASICS
MATH BASICS … 67
Basic Arithmetic . . . All about Numbers . . . More about Numbers . . .
The Concept of Zero . . . Basic Mathematical Operations . . . Fractions
FOUNDATIONS OF MATHEMATICS … 103
Foundations and Logic . . . Mathematical and Formal Logic . . .
Axiomatic System . . . Set Theory
ALGEBRA … 131
The Basics of Algebra . . . Algebra Explained . . . Algebraic
Operations . . . Exponents and Logarithms . . . Polynomial
Equations . . . More Algebra . . . Abstract Algebra
GEOMETRY AND TRIGONOMETRY … 165
Geometry Beginnings . . . Basics of Geometry . . . Plane Geometry
. . . Solid Geometry . . . Measurements and Transformations . . .
Analytic Geometry . . . Trigonometry . . . Other Geometries
MATHEMATICAL ANALYSIS … 209
Analysis Basics . . . Sequences and Series . . . Calculus Basics . . .
Differential Calculus . . . Integral Calculus . . . Differential
Equations . . . Vector and Other Analyses
APPLIED MATHEMATICS … 243
Applied Mathematics Basics . . . Probability Theory . . . Statistics . . .
Modeling and Simulation . . . Other Areas of Applied Mathematics
viii
M S E C
ATH IN CIENCE AND NGINEERING O
N
T
E
N
T
MATH IN THE PHYSICAL S
SCIENCES … 275
Physics and Mathematics . . . Classical Physics and Mathematics . . .
Modern Physics and Mathematics . . . Chemistry and Math . . .
Astronomy and Math
MATH IN THE NATURAL
SCIENCES … 295
Math in Geology . . . Math in Meteorology . . . Math in Biology . . .
Math and the Environment
MATH IN ENGINEERING … 323
Basics of Engineering . . . Civil Engineering and Mathematics . . .
Mathematics and Architecture . . . Electrical Engineering and
Materials Science . . . Chemical Engineering . . . Industrial and
Aeronautical Engineering
MATH IN COMPUTING … 347
Early Counting and Calculating Devices . . . Mechanical and
Electronic Calculating Devices . . . Modern Computers and
Mathematics . . . Applications
ix