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The Handy Math Answer Book MathFM 8/22/07 9:27 AM Page 1 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 Reference and 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. MathFM 8/22/07 9:27 AM Page 2 The Handy Answer Book Series® The Handy Answer Book for Kids (and Parents) The Handy Biology Answer Book 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 The Handy Presidents Answer Book 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. MathFM 8/22/07 9:27 AM Page 3 THE HANDY MATH ANSWER BOOK MathFM 8/22/07 9:27 AM Page 4 MathFM 8/22/07 9:27 AM Page 5 THE HANDY ANSWER BOOK Patricia Barnes-Svarney and Thomas E. Svarney Detroit MathFM 8/22/07 9:27 AM Page 6 THE Copyright © 2006 by Visible Ink Press® This publication is a creative work fully protected by all applicable copyright laws, as well as by misappropriation, trade secret, unfair competition, and other appli- HANDY cable laws. No part of this book may be reproduced in any form without permission in writ- MATH 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. Visible Ink Press® 43311 Joy Road #414 BOOK Canton, MI 48187-2075 Visible Ink Press is a trademark of Visible Ink Press LLC. Most Visible Ink Press books are available at special quantity discounts when pur- chased in bulk by corporations, organizations, or groups. Customized printings, special imprints, messages, and excerpts can be produced to meet your needs. For more information, contact Special Markets Director, Visible Ink Press, at www.visibleink.com. Art Director: Mary Claire Krzewinski 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 at casino used by permission of Taxi/Getty Images; nautilus used by permission of The Image Bank/Getty Images. Back cover images of mathematician used by permission of Stone/Getty Images; card game used by permission of The Image Bank/Getty Images. Cataloging-in-Publication Data is on file with the Library of Congress. Printed in the United States of America All rights reserved 10 9 8 7 6 5 4 3 2 1 MathFM 8/22/07 9:27 AM Page 7 Contents INTRODUCTION xi ACKNOWLEDGMENTS xiii HISTORY 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 MathFM 8/22/07 9:27 AM Page 8 THE BASICS 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 MathFM 8/22/07 9:27 AM Page 9 CONTENTS MATH IN SCIENCE AND ENGINEERING MATH IN THE PHYSICAL 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 MathFM 8/22/07 9:27 AM Page 10 MATH ALL AROUND US MATH IN THE HUMANITIES … 373 Math and the Fine Arts . Math and the Social Sciences . Math, Religion, and Mysticism . Math in Business and Economics . Math in Medicine and Law EVERYDAY MATH … 397 Numbers and Math in Everyday Life . Math and the Outdoors . Math, Numbers, and the Body . Math and the Consumer’s Money . Math and Traveling RECREATIONAL MATH … 421 Math Puzzles . Mathematical Games . Card and Dice Games . Sports Numbers . Just for Fun MATHEMATICAL RESOURCES … 443 Educational Resources . Organizations and Societies . Museums . Popular Resources . Surfing the Internet APPENDIX 1: MEASUREMENT SYSTEMS AND CONVERSION FACTORS 463 APPENDIX 2: LOG TABLE IN BASE 10 FOR THE NUMBERS 1 THROUGH 10 469 APPENDIX 3: COMMON FORMULAS FOR CALCULATING AREAS AND VOLUMES OF SHAPES 479 INDEX 483 x Handy Math FM 8/19/07 5:17 PM Page xi Introduction “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 We’ve all seen it. We’ve all experienced it, many times without knowing it. It’s in the design of a beautiful stained-glass window in the middle of an Austrian cathedral. It’s in the large and small workings of a car, computer, or space shuttle. It’s in the inno- cent statement of a child asking, “How old are you?” By now you’ve probably guessed what “it” is: mathematics. Mathematics is everywhere. Sometimes it’s as subtle as the symmetry of a butter- fly’s wings. Sometimes it’s as blatant as the U.S. debt figures displayed on a sign out- side the Internal Revenue Service building in New York City. Numbers sneak into our lives. They are used to determine a prescription for eye- glasses; they reveal blood pressure, heart rate, and cholesterol levels, too. Numbers are used so you can follow a bus, train, or plane schedule; or they can help you figure out when your favorite store, restaurant, or library is open. In the home, numbers are used for recipes, figuring out the voltage on a circuit in an electric switchbox, and measuring a room for a carpet. Probably the most familiar connection we have to numbers is in our daily use of money. Numbers, for instance, let you know whether you’re getting a fair deal on that morning cup of cappuccino. The Handy Math Answer Book is your introduction to the world of numbers, from their long history (and hints of the future) to how we use math in our everyday lives. With more than 1,000 questions and answers in The Handy Math Answer Book (1,002, to be mathematically precise) and over 100 photographs, 70 illustrations, and dozens of equations to help explain or provide examples of fundamental mathematical princi- ples, you’ll cover a lot of ground in just one book! Handy Math is split into four sections: “The History” includes famous (and some- times infamous) people, places, and objects of mathematical importance; “The Basics” xi Handy Math FM 8/19/07 5:17 PM Page xii explains the various branches of mathematics, from fundamental arithmetic to com- plex calculus; “Math in Science and Engineering” describes how relevant math is to such fields as architecture, the natural sciences, and even art; and “Math All Around Us” shows how much math is part of our daily lives, including everything from balanc- ing a checkbook to playing the slots in Las Vegas. The subject of math—and its many connections—is immense. After all, over two thousand years ago the Greek mathematician Euclid wrote thirteen books about geometry and other fields of mathematics (the famous Elements).
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