Mathematics

218 Pages·2002·10.97 MB·English

by  Barry Max Brandenberger

mathematics
EDITORIAL BOARD
Editor in Chief
Barry Max Brandenberger, Jr.
Curriculum and Instruction Consultant, Cedar Park, Texas
Associate Editor
Lucia Romberg McKay, Ph.D.
Mathematics Education Consultant, Port Aransas, Texas
Consultants
L. Ray Carry, Ph.D.
Pamela D. Garner
EDITORIAL AND PRODUCTION STAFF
Cindy Clendenon, Project Editor
Linda Hubbard, Editorial Director
Betz Des Chenes, Managing Editor
Alja Collar, Kathleen Edgar, Monica Hubbard, Gloria Lam, Kristin May,
Mark Mikula, Kate Millson, Nicole Watkins, Contributing Editors
Michelle DiMercurio, Senior Art Director
Rita Wimberley, Buyer
Bill Atkins, Phil Koth, Proofreaders
Lynne Maday, Indexer
Barbara J. Yarrow, Manager, Imaging and Multimedia Content
Robyn V. Young, Project Manager, Imaging and Multimedia Content
Pam A. Reed, Imaging Coordinator
Randy Bassett, Imaging Supervisor
Leitha Etheridge-Sims, Image Cataloger
Maria L. Franklin, Permissions Manager
Lori Hines, Permissions Assistant
Consulting School
Douglas Middle School, Box Elder, South Dakota Teacher: Kelly Lane
Macmillan Reference USA
Elly Dickason, Publisher
Hélène G. Potter, Editor in Chief
ii
mathematics
2
VOLUME
Da-Lo
Barry Max Brandenberger, Jr., Editor in Chief
Copyright © 2002 by Macmillan Reference USA,
an imprint of the Gale Group
All rights reserved. No part of this book may be reproduced or transmitted
in any form or by any means, electronic or mechanical, including photo-
copying, recording, or by any information storage and retrieval system, with-
out permission in writing from the Publisher.
Macmillan Reference USA Macmillan Reference USA
300 Park Avenue South 27500 Drake Rd.
New York, NY 10010 Farmington Hills, MI 48331-3535
Library of Congress Cataloging-in-Publication Data
Mathematics / Barry Max Brandenberger, Jr., editor in chief.
p. cm.
Includes bibliographical references and index.
ISBN 0-02-865561-3 (set : hardcover : alk. paper) - ISBN 0-02-865562-1 (v. 1 : alk. paper)
ISBN 0-02-865563-X (v. 2 : alk. paper) - ISBN 0-02-865564-8 (v. 3 : alk. paper) -
ISBN 0-02-865565-6 (v. 4 : alk. paper)
1. Mathematics-Juvenile literature. [1. Mathematics.] I. Brandenberger, Barry Max, 1971-
QA40.5 .M38 2002
510-dc21 00-045593
Printed in the United States of America
1 2 3 4 5 6 7 8 9 10
Table of Contents
VOLUME 1: Brain, Human
Bush, Vannevar
Preface
List of Contributors C
Calculators
A Calculus
Abacus Calendar, Numbers in the
Absolute Zero Carpenter
Accountant Carroll, Lewis
Accuracy and Precision Cartographer
Agnesi, Maria Gaëtana Census
Agriculture Central Tendency, Measures of
Air Traffic Controller Chaos
Algebra Cierva Codorniu, Juan de la
Algebra Tiles Circles, Measurement of
Algorithms for Arithmetic City Planner
Alternative Fuel and Energy City Planning
Analog and Digital Comets, Predicting
Angles, Measurement of Communication Methods
Angles of Elevation and Depression Compact Disc, DVD, and MP3
Technology
Apollonius of Perga
Computer-Aided Design
Archaeologist
Computer Analyst
Archimedes
Computer Animation
Architect
Computer Graphic Artist
Architecture
Computer Information Systems
Artists
Computer Programmer
Astronaut
Computer Simulations
Astronomer
Computers and the Binary System
Astronomy, Measurements in
Computers, Evolution of Electronic
Athletics, Technology in
Computers, Future of
Computers, Personal
B
Congruency, Equality, and Similarity
Babbage, Charles Conic Sections
Banneker, Benjamin Conservationist
Bases Consistency
Bernoulli Family Consumer Data
Boole, George Cooking, Measurement of
Bouncing Ball, Measurement of a Coordinate System, Polar
v
Table of Contents
Coordinate System, Three-Dimensional Flight, Measurements of
Cosmos Form and Value
Cryptology Fractals
Cycling, Measurements of
Fraction Operations
Fractions
PHOTO AND ILLUSTRATION CREDITS
GLOSSARY Functions and Equations
TOPIC OUTLINE
G
VOLUME ONE INDEX
Galileo Galilei
Games
VOLUME 2:
Gaming
Gardner, Martin
D
Genome, Human
Dance, Folk Geography
Data Analyst Geometry Software, Dynamic
Data Collxn and Interp
Geometry, Spherical
Dating Techniques
Geometry, Tools of
Decimals
Germain, Sophie
Descartes and his Coordinate System
Global Positioning System
Dimensional Relationships
Golden Section
Dimensions
Grades, Highway
Distance, Measuring
Graphs
Division by Zero
Graphs and Effects of Parameter
Dürer, Albrecht
Changes
E
H
Earthquakes, Measuring
Heating and Air Conditioning
Economic Indicators
Einstein, Albert Hollerith, Herman
Electronics Repair Technician Hopper, Grace
Encryption Human Body
End of the World, Predictions of Human Genome Project
Endangered Species, Measuring Hypatia
Escher, M. C.
Estimation I
Euclid and his Contributions
IMAX Technology
Euler, Leonhard
Induction
Exponential Growth and Decay
Inequalities
Infinity
F
Insurance agent
Factorial
Integers
Factors
Interest
Fermat, Pierre de
Interior Decorator
Fermat’s Last Theorem
Fibonacci, Leonardo Pisano Internet
Field Properties Internet Data, Reliability of
Financial Planner Inverses
vi
Table of Contents
K Morgan, Julia
Knuth, Donald Mount Everest, Measurement of
Kovalevsky, Sofya Mount Rushmore, Measurement of
Music Recording Technician
L
N
Landscape Architect
Nature
Leonardo da Vinci
Navigation
Light
Negative Discoveries
Light Speed
Nets
Limit
Newton, Sir Isaac
Lines, Parallel and Perpendicular
Number Line
Lines, Skew
Number Sets
Locus
Number System, Real
Logarithms
Numbers: Abundant, Deficient, Perfect,
Lotteries, State
and Amicable
Lovelace, Ada Byron
Numbers and Writing
Photo and Illustration Credits Numbers, Complex
Glossary Numbers, Forbidden and Superstitious
Topic Outline Numbers, Irrational
Volume Two Index Numbers, Massive
Numbers, Rational
Numbers, Real
VOLUME 3: Numbers, Tyranny of
Numbers, Whole
Nutritionist
M
Mandelbrot, Benoit B. O
Mapping, Mathematical
Ozone Hole
Maps and Mapmaking
Marketer P
Mass Media, Mathematics and the
Pascal, Blaise
Mathematical Devices, Early
Patterns
Mathematical Devices, Mechanical
Percent
Mathematics, Definition of
Permutations and Combinations
Mathematics, Impossible
Pharmacist
Mathematics, New Trends in Photocopier
Mathematics Teacher Photographer
Mathematics, Very Old Pi
Matrices Poles, Magnetic and Geographic
Measurement, English System of Polls and Polling
Measurement, Metric System of Polyhedrons
Measurements, Irregular Population Mathematics
Mile, Nautical and Statute Population of Pets
Millennium Bug Postulates, Theorems, and Proofs
Minimum Surface Area Powers and Exponents
Mitchell, Maria Predictions
Möbius, August Ferdinand Primes, Puzzles of
vii
Table of Contents
Probability and the Law of Large Numbers Space, Commercialization of
Probability, Experimental Space Exploration
Probability, Theoretical Space, Growing Old in
Problem Solving, Multiple Approaches to Spaceflight, Mathematics of
Proof Sports Data
Puzzles, Number Standardized Tests
Pythagoras Statistical Analysis
Step Functions
Q Stock Market
Stone Mason
Quadratic Formula and Equations
Sun
Quilting
Superconductivity
Surveyor
R
Symbols
Radical Sign
Symmetry
Radio Disc Jockey
Randomness
T
Rate of Change, Instantaneous
Telescope
Ratio, Rate, and Proportion
Television Ratings
Restaurant Manager
Temperature, Measurement of
Robinson, Julia Bowman
Tessellations
Roebling, Emily Warren
Tessellations, Making
Roller Coaster Designer
Time, Measurement of
Rounding
Topology
Photo and Illustration Credits Toxic Chemicals, Measuring
Glossary Transformations
Topic Outline Triangles
Volume Three Index Trigonometry
Turing, Alan
VOLUME 4:
U
Undersea Exploration
S
Universe, Geometry of
Scale Drawings and Models
Scientific Method, Measurements and the
V
Scientific Notation
Variation, Direct and Inverse
Sequences and Series
Vectors
Significant Figures or Digits
Virtual Reality
Slide Rule
Vision, Measurement of
Slope
Volume of Cone and Cylinder
Solar System Geometry, History of
Solar System Geometry, Modern
W
Understandings of
Solid Waste, Measuring Weather Forecasting Models
Somerville, Mary Fairfax Weather, Measuring Violent
Sound Web Designer
viii
Table of Contents
Z Topic Outline
Zero Cumulative Index
Photo and Illustration Credits
Glossary
ix
Dance, Folk
D
Both mathematics and dance are languages that use symbols to convey ideas
and expressions. Mathematics uses written symbols to represent abstrac-
tions so that users can arrive at a greater understanding of a problem with-
out ambiguity. Dancers use abstract symbols to represent thoughts, ambiguity the quality of
feelings, emotions, and ideas, and these symbols may be interpreted in mul- doubtfulness or uncer-
tainty
tiple ways. Both disciplines rely to a large extent on pattern recognition.
abstract having only
Many forms of dance, such as classical ballet, involve complex patterns intrinsic form
and take years of practice to master. Yet other forms of dance use everyday
movements with more simplistic patterns. For example, folk dances have
evolved from common movements of work and play.
Although folk dances require concentration and focus, their use of every-
day movement invites observers to participate. Similarly, mathematics can
be studied at the basic level of arithmetic, which is used to make simple
transactions and to understand how things work. More advanced mathe-
matics, such as calculus, chaos theory, or abstract algebra require years calculus a method of
to master. dealing mathematically
with variables that may
be changing continu-
Discreteness in Mathematics and Dance
ously with respect to
each other
Many dances are based on a simple method of counting and discrete se-
chaos theory the quali-
quences, which enables participants to recognize and learn a variety of
tative study of unstable
dances. The word “discrete” also has a common, similar usage in mathe- aperiodic behavior in
matics. Discrete mathematics involves counting separate elements, such as deterministic nonlinear
dynamical systems
the number of arrangements of letters on a license place, or the number of
ways that a presidential candidate can visit all fifty states. Solutions in dis- abstract algebra the
branch of algebra deal-
crete mathematics can be only whole units. Discrete math is therefore one
ing with groups, rings,
of the most accessible areas of modern mathematics since many of the ques-
fields, Galois sets, and
tions are easy for anyone to understand. number theory
Contradancing. Contradancing is a popular form of folk dance in the discrete composed of
distinct elements
United States that illustrates the mathematics of dance. Its origins go back
to colonial days, and its roots can be traced to English country dances.
Contradancing, which shares elements of traditional square dancing, is set dancing a form of
dance in which dancers
a form of set dancingin which a dancer’s position relative to another dancer
are guided through a
traces patterns on the dance floor. As in most dancing, timing is crucial, as
series of moves by a
is the ability to rapidly carry out called instructions. caller
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