Table Of Contentmathematics
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
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mathematics
VOL U M E 1
Ab–Cy
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
Preface
Mathematics has been defined as the “universal language of numbers,”
a language whose basic principles remain the same for all users. Many rou-
tine activities, from balancing a checkbook to measuring ingredients for a
recipe, require a certain familiarity with mathematical concepts and appli-
cations. In Macmillan’s Mathematics encyclopedia, users will learn more
about the function of mathematics in everyday life, as well as its role as a
tool for measurement, data analysis, and technological development. Inter-
disciplinary in scope, the encyclopedia provides students with a clear and
comprehensive introduction to this vast topic through nearly three hundred
entries commissioned especially for the set.
A Broader Look at Mathematics
For many people, mathematics and its basic disciplines—such as alge-
bra, geometry, and trigonometry—are subjects of fear and dread. The goal
of the Mathematics encyclopedia is to make these topics more accessible and
interesting to students and the general user. Readers will learn that mathe-
matics is much more than numbers alone—it is also an integral part of his-
tory and culture. Biographical entries highlight mathematicians who have
made significant contributions to the field. Over thirty career-related arti-
cles offer examples of mathematics “on the job,” whether it’s a nutritionist
calculating dietary needs or a photographer compensating for low-light con-
ditions. Entries on applications explore the role of mathematics in our mod-
ern world, from everyday conveniences to global communication methods
and a multitude of scientific and technological advances.
Organization of the Material
The authors who contributed entries to Mathematics bring a variety of
expertise to the subject, and include members of academic institutions, math
educators, and curriculum specialists. Contributors used their subject knowl-
edge to write entries that are authoritative and up-to-date, but free of overly
technological terms or scientific jargon. Many entries are illustrated, and
numerous equations, tables, figures, and sidebars help illuminate the text.
Unfamiliar terms and concepts are highlighted and defined in the margin,
while cross-references direct users to articles of related interest. Most en-
tries feature a selected bibliography, including Internet resources. Each vol-
ume includes a topical outline, glossary, and index, with a cumulative index
to the entire set appearing in volume 4.
Acknowledgments and Thanks
I would like to acknowledge the support of my editorial advisors, Pam
Garner and Dr. Ray Carry, for their valuable contributions to the scope and
v
Preface
overall design of this project. I would also like to thank Hélène Potter and
Cindy Clendenon for their unending patience and guidance in making the
initial ideas for this encyclopedia into a real product. Finally, I would like
to thank my associate editor, Dr. Lucia McKay, for her remarkable mathe-
matical and literary mind, which remained sharp and focused even after re-
viewing hundreds of articles. I cannot thank her enough.
Barry Max Brandenberger, Jr.
v i
Contributors
Leslie Aspinwall Brook E. Hall Dana Mackenzie
Florida State University California State University, Santa Cruz, California
Tallahassee, Florida Sacramento Teresa D. Magnus
William Arthur Atkins Sacramento, California Rivier College
Galesburg, Illinois Bob Horton Nashua, New Hampshire
Arth
Uunri vJe. rBsiatyr ooof dIlylinois at Urbana- Clemmssoonn U, Sniovuetrhsi tCy arolina KelAlyu Jst. inM, aTretxinason
Champaign Dick Jardine
Champaign, Illinois Keene State College Nelson Maylone
Don Barry Keene, New Hampshire Eastern Michigan University
Phillips Academy Iris DeLoach Johnson Ypsilanti, Michigan
Andover, Massachusetts Miami University Lucia McKay
Darin Beigie Oxford, Ohio Port Aransas, Texas
Harvard-Westlake Middle School Arthur V. Johnson II Minerva Mercado-Feliciano
Los Angeles, California Boston University Indiana Department of
Max Brandenberger Boston, Massachusetts Environmental Management
Cedar Park, Texas
Loretta Anne Kelley Indianapolis, Indiana
Óscar Chávez San Francisco, California Michelle R. Michael
U
Conliuvemrsbitiya ,o Mf Missisosouurrii Naomi Klarreich Austin, Texas
Cleveland, Ohio Susan Strain Mockert
Mic
Uhnaeivl eCrsoithy eonf Aizu Philip Edward Koth Indianapolis, Indiana
Aizu-Wakamatsu, Japan East Peoria, Illinois J. William Moncrief
Curtis Cooper Jane Keiser Krumpe Brevard College
Central Missouri State Universitiy Miami University Brevard, North Carolina
Warrensburg, Missouri Oxford, Ohio Barbara M. Moskal
Paula C. Davis Harry J. Kuhman Colorado School of Mines
Grand Forks, North Dakota Apex, North Carolina Golden, Colorado
John J. Edgell, Jr. Rafiq Ladhani Phillip Nissen
Southwest Texas State University Staten Island, New York Riverwood High School and Georgia
San Marcos, Texas Frederick Landwehr State University
Thomas G. Edwards Austin, Texas Atlanta, Georgia
Wayne State University Randy Lattimore Michael J. O’Neal
Detroit, Michigan Wayne State University Moscow, Idaho
Demetria Ennis-Cole Detroit, Michigan Michael Ota
University of North Texas
Denton, Texas A. Darien Lauten Austin, Texas
Bar
Ut Gnieverstisty of Wyoming RNiavsiehru Ca,o Nlleegwe Hampshire DenAiusest iPnr, eTnedxearsgast
Laramie, Wyoming Jacq
Tueemlipnle ULenoivnearrsidty Robert J. Quinn
Albert Goetz Philadelphia, Pennsylvania University of Nevada, Reno
Ramaz School Reno, Nevada
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Clipoel uwMm Y.b Goiar okCl,d oNlfleeedgwe r CYhoircakgo Center EdwDNaarnsdhi eLul a’WH, Neobmestwmer H eCdaoimelluepgsehire GayS opAur.ti nhRwgafegiseatl ndM, iMssoiussroi uSrtiate University
for Book and Paper Arts Alan Lipp
Chicago, Illinois Williston Northampton School Elliot Richmond
Shirley B. Gray Easthampton, Massachusetts Education Consultants
California State University, Los Rose Kathleen Lynch Austin, Texas
Angeles Indiana University Stephen Robinson
Los Angeles, California Bloomington, Indiana San Dimas, California
v i i
Contributors
F. Arnold Romberg Shai Simonson Locord D. Wilson
La Grange, Texas Stonehill College Jackson State University
North Easton, Massachusetts Jackson, Mississippi
Lorraine Savage
Manchester, New Hampshire Laura Snyder Alice Romberg Wood
Sierra Vista, Arizona Bellwood, Nebraska
Daniel Scher
New York University Elizabeth Sweeney John R. Wood
New York, New York Clayton Middle School Bellwood, Nebraska
Reno, Nevada
Marilyn Schwader Sonia Woodbury
Clarity of Vision Writing & Design Marzieh Thomasian University of Utah
Portland, Oregon Austin, Texas Salt Lake City, Utah
Paul Shotsberger Stanislaus Noel Ting Richard B. Worth
University of North Carolina at Evry, France Indiana Department of
Wilmington Environmental Management
Joan Vernikos
Wilmington, North Carolina Indianapolis, Indiana
Thirdage LLC
Marilyn K. Simon Alexandria, Virginia
Walden University
Minneapolis, MN
vi i i
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
Apollonius of Perga Technology
Archaeologist Computer-Aided Design
Archimedes Computer Analyst
Architect Computer Animation
Architecture Computer Graphic Artist
Artists Computer Information Systems
Astronaut Computer Programmer
Astronomer Computer Simulations
Astronomy, Measurements in Computers and the Binary System
Athletics, Technology in Computers, Evolution of Electronic
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
ix
