Real-life math

653 Pages·2006·9.392 MB·English

by  K. Lee Lerner, Brenda Wilmoth Lerner

Real-
Real-
Life
Life
Math
Math
RReeaall--
LLiiffee
MMaatthh
VVoolluummee 11:: AA––LL
K. Lee Lerner & Brenda Wilmoth Lerner,
Editors
Real-
Real-
Life
Life
Math
Math
Volume 2: M–Z
Volume 2: M–Z
Field of Application Index
Field of Application Index
General Index
General Index
K. Lee Lerner & Brenda Wilmoth Lerner,
Editors
Real-Life Math
K. Lee Lerner and Brenda Wilmoth Lerner, Editors
Project Editor Indexing Composition
Kimberley A. McGrath Factiva, a Dow Jones & Reuters Company Evi Seoud, Mary Beth Trimper
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LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA
Real-life math / K. Lee Lerner and Brenda Wilmoth Lerner, editors.
p. cm.
Includes bibliographical references and index.
ISBN 0-7876-9422-3 (set : hardcover: alk. paper)—
ISBN 0-7876-9423-1 (v. 1)—ISBN 0-7876-9424-X (v. 2)
1. Mathematics—Encyclopedias.
I. Lerner, K. Lee. II. Lerner, Brenda Wilmoth.
QA5.R36 2006
510’.3—dc22 2005013141
This title is also available as an e-book, ISBN 1414404999 (e-book set).
ISBN: 0-7876-9422-3 (set); 0-7876-9423-1 (v1); 0-7876-9424-X (v2)
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Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
Entries (With Areas ofDiscussion) . . . . . . . vii
Introduction . . . . . . . . . . . . . . xix
List ofAdvisors and Contributors . . . . . . . xxi
Entries . . . . . . . . . . . . . . . 1
Volume 1: A–L
Addition . . . . . . . . . . . . . . . 1
Algebra . . . . . . . . . . . . . . . 9
Algorithms . . . . . . . . . . . . . . 26
Architectural Math . . . . . . . . . . . . 33
Area . . . . . . . . . . . . . . . . 45
Average. . . . . . . . . . . . . . . . 51
Table of
Base . . . . . . . . . . . . . . . . 59
Business Math . . . . . . . . . . . . . 62 Contents
Calculator Math . . . . . . . . . . . . 69
Calculus . . . . . . . . . . . . . . . 80
Calendars . . . . . . . . . . . . . . . 97
Cartography. . . . . . . . . . . . . .100
Charts. . . . . . . . . . . . . . . .107
Computers and Mathematics . . . . . . . .114
Conversions . . . . . . . . . . . . . .122
Coordinate Systems . . . . . . . . . . .131
Decimals . . . . . . . . . . . . . . .138
Demographics . . . . . . . . . . . . .141
Discrete Mathematics . . . . . . . . . .144
Division . . . . . . . . . . . . . . .149
Domain and Range . . . . . . . . . . .156
Elliptic Functions . . . . . . . . . . . .159
Estimation . . . . . . . . . . . . . .161
Exponents . . . . . . . . . . . . . .167
Factoring. . . . . . . . . . . . . . .180
Financial Calculations,Personal . . . . . . .184
Fractals . . . . . . . . . . . . . . .198
Fractions . . . . . . . . . . . . . . .203
Functions. . . . . . . . . . . . . . .210
Game Math . . . . . . . . . . . . . .215
Game Theory . . . . . . . . . . . . .225
Geometry. . . . . . . . . . . . . . .232
Graphing. . . . . . . . . . . . . . .248
Imaging . . . . . . . . . . . . . . .262
Information Theory . . . . . . . . . . .269
Inverse . . . . . . . . . . . . . . . .278
Iteration . . . . . . . . . . . . . . .284
Linear Mathematics . . . . . . . . . . .287
Logarithms . . . . . . . . . . . . . .294
Logic . . . . . . . . . . . . . . . .300
v
R E A L - L I F E M A T H
Table of Contents
Rounding . . . . . . . . . . . . . .449
Volume 2: M–Z
Rubric. . . . . . . . . . . . . . . .453
Matrices and Determinants. . . . . . . . .303 Sampling . . . . . . . . . . . . . . .457
Measurement . . . . . . . . . . . . .307 Scale . . . . . . . . . . . . . . . .465
Medical Mathematics. . . . . . . . . . .314 Scientific Math . . . . . . . . . . . . .473
Modeling. . . . . . . . . . . . . . .328 Scientific Notation . . . . . . . . . . .484
Multiplication . . . . . . . . . . . . .335 Sequences,Sets,and Series . . . . . . . . .491
Music and Mathematics . . . . . . . . . .343 Sports Math . . . . . . . . . . . . . .495
Nature and Numbers . . . . . . . . . . .353 Square and Cube Roots . . . . . . . . . .511
Negative Numbers. . . . . . . . . . . .356 Statistics . . . . . . . . . . . . . . .516
Number Theory . . . . . . . . . . . .360 Subtraction . . . . . . . . . . . . . .529
Odds . . . . . . . . . . . . . . . .365 Symmetry . . . . . . . . . . . . . .537
Percentages . . . . . . . . . . . . . .372 Tables . . . . . . . . . . . . . . . .543
Perimeter. . . . . . . . . . . . . . .385 Topology . . . . . . . . . . . . . . .553
Perspective . . . . . . . . . . . . . .389 Trigonometry . . . . . . . . . . . . .557
Photography Math . . . . . . . . . . .398 Vectors . . . . . . . . . . . . . . .568
Plots and Diagrams . . . . . . . . . . .404 Volume . . . . . . . . . . . . . . .575
Powers . . . . . . . . . . . . . . .416 Word Problems. . . . . . . . . . . . .583
Prime Numbers. . . . . . . . . . . . .420 Zero-sum Games . . . . . . . . . . . .595
Probability . . . . . . . . . . . . . .423
Glossary . . . . . . . . . . . . . . .599
Proportion . . . . . . . . . . . . . .430
Field ofApplication Index . . . . . . . . .605
Quadratic,Cubic,and Quartic Equations . . . .438
Ratio . . . . . . . . . . . . . . . .441 General Index . . . . . . . . . . . . .609
vi
R E A L - L I F E M A T H
Addition
Financial Addition. . . . . . . . . . . . 4
Geometric Progression . . . . . . . . . . 6
Poker,Probability,and Other Uses ofAddition . . 5
Sports and Fitness Addition. . . . . . . . . 3
Using Addition to Predict and Entertain . . . . 6
Algebra
Art . . . . . . . . . . . . . . . . . 21
Building Skyscrapers . . . . . . . . . . . 19
Buying Light Bulbs . . . . . . . . . . . 20
College Football . . . . . . . . . . . . 14
Entries
Crash Tests . . . . . . . . . . . . . . 18
Fingerprint Scanners . . . . . . . . . . . 22 (With Areas
Flying an Airplane. . . . . . . . . . . . 16
of Discussion)
Fundraising . . . . . . . . . . . . . . 19
Personal Finances . . . . . . . . . . . . 13
Population Dynamics. . . . . . . . . . . 22
Private Space Travel . . . . . . . . . . . 24
Skydiving. . . . . . . . . . . . . . . 17
Teleportation. . . . . . . . . . . . . . 23
UPC Barcodes . . . . . . . . . . . . . 15
Algorithms
Archeology . . . . . . . . . . . . . . 27
Artificial Intelligence . . . . . . . . . . . 32
Computer Programming . . . . . . . . . 27
Credit Card Fraud Detection . . . . . . . . 27
Cryptology . . . . . . . . . . . . . . 28
Data Mining. . . . . . . . . . . . . . 28
Digital Animation and Digital Model Creation . . 28
DNA or Genetic Analysis . . . . . . . . . 28
Encryption and Encryption Devices . . . . . . 28
The Genetic Code . . . . . . . . . . . . 30
Imaging . . . . . . . . . . . . . . . 29
Internet Data Transmission. . . . . . . . . 29
Linguistics,the Study ofLanguage . . . . . . 31
Mapping . . . . . . . . . . . . . . . 30
Market or Sales Analysis . . . . . . . . . . 30
Operational Algorithms . . . . . . . . . . 27
Security Devices . . . . . . . . . . . . 31
Sports Standings and Seedings. . . . . . . . 31
Tax Returns . . . . . . . . . . . . . . 31
Architectural Math
Architectural Concepts in Wheels. . . . . . . 43
Architectural Symmetry in Buildings . . . . . 38
vii
R E A L - L I F E M A T H
Entries (With Areas of Discussion)
Architecture . . . . . . . . . . . . . . 36
Base
Astronomy . . . . . . . . . . . . . . 43
Ergonomics . . . . . . . . . . . . . . 41 Base 2 and Computers . . . . . . . . . . 60
Geometry,Basic Forms and Shapes of . . . . . 40
Golden Rectangle and Golden Ratio . . . . . . 38
Business Math
Grids,Use of . . . . . . . . . . . . . 37
Jewelry . . . . . . . . . . . . . . . 41
Accounting . . . . . . . . . . . . . . 63
Measurement . . . . . . . . . . . . . 35
Budgets . . . . . . . . . . . . . . . 63
Proportion . . . . . . . . . . . . . . 34
Earnings . . . . . . . . . . . . . . . 66
Ratio . . . . . . . . . . . . . . . . 33
Interest . . . . . . . . . . . . . . . 67
Ratio and Proportion,Use of . . . . . . . . 38
Payroll. . . . . . . . . . . . . . . . 65
Scale Drawing . . . . . . . . . . . . . 34
Profits. . . . . . . . . . . . . . . . 66
Space,Use Of . . . . . . . . . . . . . 37
Sports . . . . . . . . . . . . . . . . 38
Symmetry . . . . . . . . . . . . . . 34 Calculator Math
Symmetry in City Planning. . . . . . . . . 41
Technology . . . . . . . . . . . . . . 41 Bridge Construction . . . . . . . . . . . 76
Textile and Fabrics. . . . . . . . . . . . 43 Combinatorics . . . . . . . . . . . . . 77
Compound Interest . . . . . . . . . . . 74
Financial Transactions . . . . . . . . . . 73
Area Measurement Calculations . . . . . . . . . 75
Nautical Navigation . . . . . . . . . . . 73
Area ofa Rectangle . . . . . . . . . . . 45
Random Number Generator . . . . . . . . 75
Areas ofCommon Shapes . . . . . . . . . 46
Supercomputers . . . . . . . . . . . . 78
Areas ofSolid Objects . . . . . . . . . . 46
Understanding Weather . . . . . . . . . . 77
Buying by Area . . . . . . . . . . . . . 47
Car Radiators . . . . . . . . . . . . . 48
Cloud and Ice Area and Global Warming . . . . 47 Calculus
Drug Dosing . . . . . . . . . . . . . 46
Applications ofDerivatives . . . . . . . . . 86
Filtering . . . . . . . . . . . . . . . 47
Derivative . . . . . . . . . . . . . . 81
Solar Panels . . . . . . . . . . . . . . 49
Functions . . . . . . . . . . . . . . 81
Surveying . . . . . . . . . . . . . . 48
Fundamental Theorem ofCalculus . . . . . . 85
Units ofArea . . . . . . . . . . . . . 45
Integral . . . . . . . . . . . . . . . 83
Integrals,Applications . . . . . . . . . . 91
Average Maxima and Minima . . . . . . . . . . . 85
Arithmetic Mean . . . . . . . . . . . . 51
The “Average”Family . . . . . . . . . . . 55 Calendars
Average Lifespan . . . . . . . . . . . . 57
Gregorian Calendar . . . . . . . . . . . 99
Averaging for Accuracy . . . . . . . . . . 55
Islamic and Chinese Calendars. . . . . . . . 99
Batting Averages . . . . . . . . . . . . 53
Leap Year. . . . . . . . . . . . . . . 99
Evolution in Action . . . . . . . . . . . 57
Geometric Mean . . . . . . . . . . . . 52
Grades. . . . . . . . . . . . . . . . 54 Cartography
How Many Galaxies? . . . . . . . . . . . 55
Insurance. . . . . . . . . . . . . . . 57 Coordinate Systems . . . . . . . . . . .103
Mean . . . . . . . . . . . . . . . . 52 GIS-Based Site Selection. . . . . . . . . .105
Median . . . . . . . . . . . . . . . 52 GPS Navigation. . . . . . . . . . . . .105
Space Shuttle Safety . . . . . . . . . . . 56 Map Projection. . . . . . . . . . . . .100
Student Loan Consolidation . . . . . . . . 56 Natural Resources Evaluation and Protection . . .105
Weighted Averages in Business. . . . . . . . 54 Scale . . . . . . . . . . . . . . . .100
Weighted Averages in Grading . . . . . . . . 54 Topographic Maps. . . . . . . . . . . .104
viii
R E A L - L I F E M A T H
Entries (With Areas of Discussion)
Longitude and John Harrison . . . . . . . .135
Charts
Modern Navigation and GPS . . . . . . . .135
Bar Charts . . . . . . . . . . . . . .109 Paper Maps ofthe World . . . . . . . . .134
Basic Charts . . . . . . . . . . . . . .107 Polar Coordinates . . . . . . . . . . . .133
Choosing the Right Type ofChart For the Data . .112 Radar Systems and Polar Coordinates . . . . .136
Clustered Column Charts . . . . . . . . .110 Vectors . . . . . . . . . . . . . . .132
Column and Bar Charts . . . . . . . . . .109
Line Charts . . . . . . . . . . . . . .107
Decimals
Pie Charts . . . . . . . . . . . . . .110
Stacked Column Charts . . . . . . . . . .110
Grade Point Average Calculations. . . . . . .139
Using the Computer to Create Charts . . . . .112
Measurement Systems . . . . . . . . . .139
X-Y Scatter Graphs . . . . . . . . . . .109
Science . . . . . . . . . . . . . . .139
Computers and Mathematics
Demographics
Algorithms . . . . . . . . . . . . . .115
Census . . . . . . . . . . . . . . .142
Binary System . . . . . . . . . . . . .114
Election Analysis . . . . . . . . . . . .141
Bits. . . . . . . . . . . . . . . . 116
Geographic Information System Technology . . .143
Bytes . . . . . . . . . . . . . . . .116
Compression. . . . . . . . . . . . . .118
Data Transmission. . . . . . . . . . . .119 Discrete Mathematics
Encryption . . . . . . . . . . . . . .120
IP Address . . . . . . . . . . . . . .117 Algorithms . . . . . . . . . . . . .145
Pixels,Screen Size,and Resolution . . . . . .117 Boolean Algebra . . . . . . . . . . . .145
Subnet Mask. . . . . . . . . . . . . .118 Combinatorial Chemistry . . . . . . . . .147
Text Code . . . . . . . . . . . . . .116 Combinatorics . . . . . . . . . . . . .145
Computer Design . . . . . . . . . . . .146
Counting Jaguars Using Probability Theory . . .147
Conversions
Cryptography . . . . . . . . . . . . .146
Finding New Drugs with Graph Theory . . . .147
Absolute Systems . . . . . . . . . . . .127
Graphs . . . . . . . . . . . . . . .146
Arbitrary Systems . . . . . . . . . . . .128
Logic,Sets,and Functions . . . . . . . . .144
Cooking or Baking Temperatures . . . . . . .127
Looking Inside the Body With Matrices. . . . .147
Derived Units . . . . . . . . . . . . .124
Matrix Algebra . . . . . . . . . . . . .146
English System . . . . . . . . . . . . .123
Number Theory . . . . . . . . . . . .145
International System ofUnits (SI) . . . . . .123
Probability Theory. . . . . . . . . . . .145
Metric Units. . . . . . . . . . . . . .123
Searching the Web. . . . . . . . . . . .146
Units Based On Physical or “Natural”
Shopping Online and Prime Numbers . . . . .147
Phenomena . . . . . . . . . . . .124
Weather Forecasting . . . . . . . . . . .126
Division
Coordinate Systems
Averages . . . . . . . . . . . . . . .152
Division and Comparison . . . . . . . . .151
3-D Systems On Ordinance Survey Maps . . . .136
Division and Distribution . . . . . . . . .150
Cartesian Coordinate Plane. . . . . . . . .132
Division,Other Uses . . . . . . . . . . .153
Changing Between Coordinate Systems . . . . .132
Practical Uses ofDivision For Students . . . . .153
Choosing the Best Coordinate System . . . . .132
Commercial Aviation . . . . . . . . . . .135
Coordinate Systems Used in Board Games . . . .134 Domain and Range
Coordinate Systems Used for Computer
Animation . . . . . . . . . . . . .134 Astronomers . . . . . . . . . . . . .157
Dimensions ofa Coordinate System . . . . . .131 Calculating Odds and Outcomes . . . . . . .157
ix
R E A L - L I F E M A T H