Real-Life Math (2 vols) - K. Lerner, B. Lerner (Thomson Gale, 2006)

Real-Life Math (2 vols) - K. Lerner, B. Lerner (Thomson Gale, 2006)

(Parte 1 de 9)

Real-

Life Math

Real-

Life Math

Real-

Life

Math Volume 1: A–L

Real-

Life

Math

Volume 1: A–L

K. Lee Lerner & Brenda Wilmoth Lerner, Editors

Real-

Life

Math

Volume 2: M–Z

Field of Application Index General Index

Real-

Life

Math

Volume 2: M–Z

Field of Application Index General Index

K. Lee Lerner & Brenda Wilmoth Lerner, Editors

Real-Life Math K. Lee Lerner and Brenda Wilmoth Lerner, Editors

Project Editor Kimberley A. McGrath

Editorial Luann Brennan, Meggin M. Condino, Madeline Harris, Paul Lewon, Elizabeth Manar

Editorial Support Services Andrea Lopeman

Indexing Factiva, a Dow Jones & Reuters Company

Rights and Acquisitions Margaret Abendroth, Timothy Sisler

Imaging and Multimedia Lezlie Light, Denay Wilding

Product Design Pamela Galbreath, Tracey Rowens

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Manufacturing Wendy Blurton, Dorothy Maki

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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. I. Lerner, Brenda Wilmoth.

510’.3—dc222005013141

QA5.R36 2006

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) Contact your Gale sales representative for ordering information.

Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

REAL-LIFE MATHv

Table of Contents

Entries (With Areas ofDiscussion)vii
Introductionxix
List ofAdvisors and Contributorsxxi
Entries1
Addition1
Algebra9
Algorithms26
Architectural Math3
Area45
Average51
Base59
Business Math62
Calculator Math69
Calculus80
Calendars97
Cartography100
Charts107
Computers and Mathematics114
Conversions122
Coordinate Systems131
Decimals138
Demographics141
Discrete Mathematics144
Division149
Domain and Range156
Elliptic Functions159
Estimation161
Exponents167
Factoring180
Financial Calculations, Personal184
Fractals198
Fractions203
Functions210
Game Math215
Game Theory225
Geometry232
Graphing248
Imaging262
Information Theory269
Inverse278
Iteration284
Linear Mathematics287
Logarithms294

Table of Contents viREAL-LIFE MATH

Matrices and Determinants303
Measurement307
Medical Mathematics314
Modeling328
Multiplication335
Music and Mathematics343
Nature and Numbers353
Negative Numbers356
Number Theory360
Odds365
Percentages372
Perimeter385
Perspective389
Photography Math398
Plots and Diagrams404
Powers416
Prime Numbers420
Probability423
Proportion430
Quadratic, Cubic, and Quartic Equations438
Ratio441
Rounding449
Rubric453
Sampling457
Scale465
Scientific Math473
Scientific Notation484
Sequences, Sets, and Series491
Sports Math495
Square and Cube Roots511
Statistics516
Subtraction529
Symmetry537
Tables543
Topology553
Trigonometry557
Vectors568
Volume575
Word Problems583
Zero-sum Games595
Glossary599
Field ofApplication Index605

Volume 2: M–Z General Index ... .......... 609

REAL-LIFE MATHvii

Entries (With Areas of Discussion)

Financial Addition4
Geometric Progression6
Sports and Fitness Addition3
Using Addition to Predict and Entertain6

Addition Poker,Probability,and Other Uses ofAddition..5

Art21
Building Skyscrapers19
Buying Light Bulbs20
College Football14
Crash Tests18
Fingerprint Scanners2
Flying an Airplane16
Fundraising19
Personal Finances13
Population Dynamics2
Private Space Travel24
Skydiving17
Teleportation23
UPC Barcodes15

Algebra

Archeology27
Artificial Intelligence32
Computer Programming27
Credit Card Fraud Detection27
Cryptology28
Data Mining28
DNA or Genetic Analysis28
Encryption and Encryption Devices28
The Genetic Code30
Imaging29
Internet Data Transmission29
Linguistics, the Study of Language31
Mapping30
Market or Sales Analysis30
Operational Algorithms27
Security Devices31
Sports Standings and Seedings31
Tax Returns31

Algorithms Digital Animation and Digital Model Creation..28

Architectural Concepts in Wheels43

Architectural Math Architectural Symmetry in Buildings.....38

Entries (With Areas of Discussion)

Architecture36
Astronomy43
Ergonomics41
Geometry,Basic Forms and Shapes of40
Golden Rectangle and Golden Ratio38
Grids, Use of37
Jewelry41
Measurement35
Proportion34
Ratio3
Ratio and Proportion,Use of38
Scale Drawing34
Space, Use Of37
Sports38
Symmetry34
Symmetry in City Planning41
Technology41
Textile and Fabrics43

viiiREAL-LIFE MATH

Area ofa Rectangle45
Areas ofCommon Shapes46
Areas ofSolid Objects46
Buying by Area47
Car Radiators48
Cloud and Ice Area and Global Warming47
Drug Dosing46
Filtering47
Solar Panels49
Surveying48
Units of Area45

Area

Arithmetic Mean51
The “Average” Family5
Average Lifespan57
Averaging for Accuracy5
Batting Averages53
Evolution in Action57
Geometric Mean52
Grades54
How Many Galaxies?5
Insurance57
Mean52
Median52
Space Shuttle Safety56
Student Loan Consolidation56
Weighted Averages in Business54
Weighted Averages in Grading54

Average

Base 2 and Computers60

Base

Accounting63
Budgets63
Earnings6
Interest67
Payroll65
Profits6

Business Math

Bridge Construction76
Combinatorics7
Compound Interest74
Financial Transactions73
Measurement Calculations75
Nautical Navigation73
Random Number Generator75
Supercomputers78
Understanding Weather7

Calculator Math

Applications of Derivatives86
Derivative81
Functions81
Fundamental Theorem ofCalculus85
Integral83
Integrals, Applications91
Maxima and Minima85

Calculus

Gregorian Calendar9
Islamic and Chinese Calendars9
Leap Year9

Calendars

Coordinate Systems103
GIS-Based Site Selection105
GPS Navigation105
Map Projection100
Scale100

Entries (With Areas of Discussion)

REAL-LIFE MATHix

Bar Charts109
Basic Charts107
Clustered Column Charts110
Column and Bar Charts109
Line Charts107
Pie Charts110
Stacked Column Charts110
Using the Computer to Create Charts112
X-Y Scatter Graphs109

Charts Choosing the Right Type ofChart For the Data..112

Algorithms115
Binary System114
Bits116
Bytes116
Compression118
Data Transmission119
Encryption120
IP Address117
Pixels, Screen Size, and Resolution117
Subnet Mask118
Text Code116

Computers and Mathematics

Absolute Systems127
Arbitrary Systems128
Cooking or Baking Temperatures127
Derived Units124
English System123
International System ofUnits (SI)123
Metric Units123
Phenomena124
Weather Forecasting126

Conversions Units Based On Physical or “Natural”

3-D Systems On Ordinance Survey Maps136
Cartesian Coordinate Plane132
Changing Between Coordinate Systems132
Choosing the Best Coordinate System132
Commercial Aviation135
Coordinate Systems Used in Board Games134
Animation134
Dimensions ofa Coordinate System131
Longitude and John Harrison135
Modern Navigation and GPS135
Paper Maps ofthe World134
Polar Coordinates133
Radar Systems and Polar Coordinates136
Vectors132

Coordinate Systems Coordinate Systems Used for Computer

Grade Point Average Calculations139
Measurement Systems139
Science139

Decimals

Census142
Election Analysis141

Demographics Geographic Information System Technology...143

Algorithms145
Boolean Algebra145
Combinatorial Chemistry147
Combinatorics145
Computer Design146
Cryptography146
Finding New Drugs with Graph Theory147
Graphs146
Logic, Sets, and Functions144
Looking Inside the Body With Matrices147
Matrix Algebra146
Number Theory145
Probability Theory145
Searching the Web146
Shopping Online and Prime Numbers147
Averages152
Division and Comparison151
Division and Distribution150
Division, Other Uses153
Practical Uses ofDivision For Students153

Division

Astronomers157

Entries (With Areas of Discussion)

Computer Control and Coordination157
Computer Science158
Engineering157
Graphs, Charts, Maps158
Physics157

xREAL-LIFE MATH

The Age ofthe Universe160
Conformal Maps159
E-Money160

Elliptic Functions

Buying a Used Car162
Carbon Dating165
Digital Imaging164
Gumball Contest163
Hubble Space Telescope165
Population Sampling164
Software Development166

Estimation

Bases and Exponents167

Exponents Body Proportions and Growth

Skinny Legs)179
Credit Card Meltdown178
Expanding Universe178
Exponential Functions168
Exponential Growth171
Exponents and Evolution174
Integer Exponents167
Interest and Inflation177
Non-Integer Exponents168
Radioactive Dating177
Radioactive Decay175
Rotting Leftovers173
Scientific Notation171

(Why Elephants Don’t Have

Codes and Code Breaking182
Distribution182
Geometry and Approximation ofSize182
and Behaviors181
Reducing Equations181
Skill Transfer182

Factoring Identification ofPatterns

Balancing a Checkbook189
Budgets188
Buying Music184
Calculating a Tip194
Car Purchasing and Payments187
Choosing a Wireless Plan187
Credit Cards185
Currency Exchange195
Investing190
Retirement Investing192
Social Security System190
Understanding Income Taxes189

Financial Calculations, Personal

Astronomy202
Building Fractals199
Cell Phone and Radio Antenna202
Computer Science202
Fractals and Nature200
Modeling Hurricanes and Tornadoes201
Nonliving Systems201
Similarity199

Fractals

Algebra205
Cooking and Baking206
Fractions and Decimals204
Fractions and Percentages204
Fractions and Voting208
Music206
Overtime Pay208
Radioactive Waste206
Rules For Handling Fractions204
Simple Probabilities207
Tools and Construction208
Types of Fractions203
What Is a Fraction?203

Fractions

Body Mass Index214
Finite-Element Models212
Functions, Described210
Functions and Relations210
Guilloché Patterns211

Entries (With Areas of Discussion)

The Million-Dollar Hypothesis212
Nuclear Waste213
Synths and Drums213

REAL-LIFE MATHxi

Basic Board Games220
Card Games218
Magic Squares221
Math Puzzles223
Other Casino Games219

Game Math

Artificial Intelligence230
Decision Theory228
eBay and the Online Auction World230
Economics229
Economics and Game Theory228
Evolution and Animal Behavior229
General Equilibrium229
Infectious Disease Therapy230
Nash Equilibrium229

Game Theory

Architecture237
Fireworks241
Fourth Dimension245
Global Positioning239
Honeycombs239
Manipulating Sound241
Pothole Covers236
Robotic Surgery245
Rubik’s Cube243
Shooting an Arrow244
Solar Systems242
Stealth Technology244

Geometry

Aerodynamics and Hydrodynamics259
Area Graphs252
Bar Graphs249
Biomedical Research258
Bubble Graphs257
Computer Network Design259
Finding Oil258
Gantt Graphs254
Global Warming257
GPS Surveying258
Line Graphs251
Physical Fitness259
Picture Graphs254
Pie Graphs252
Radar Graphs253
X-Y Graphs254

Graphing

Altering Images263
Analyzing Images263
Art267
Compression264
Creating Images263
Dance266
Forensic Digital Imaging266
Meat and Potatoes266
Medical Imaging264
Optics264
Biometrics Application264
Steganography and Digital Watermarks266

Imaging Recognizing Faces:a Controversial

Communications273
Error Correction275
Information and Meaning273
Quantum Computing276
Unequally Likely Messages271

Information Theory Information Theory in Biology and Genetics...274

Anti-Sound282
On the Eye281
Cryptography280
Definition ofan Inverse278
Fluid Mechanics and Nonlinear Design281
Inverse Functions279
The Multiplicative Inverse278
Negatives Used in Photography281
Not Exist279

Inverse The Brain and the Inverted Image Operations Where the Inverse Does

Inverse279
Stealth Submarine Communications282

Operations With More Than One Stereo ...... .......... 282

Entries (With Areas of Discussion) xiiREAL-LIFE MATH

Iteration and Business285
Iteration and Computers286
Iteration and Creativity285
Iteration and Sports284

Iteration

Earthquake Prediction289
Linear Programming291
Linear Reproduction ofMusic292
Recovering Human Motion From Video290
Virtual Tennis291

Linear Mathematics

Algebra ofPowers ofLogarithms296
Computer Intensive Applications297
Cryptography and Group Theory299
for Equipment in Space299
Developing Optical Equipment298
Using Carbon Dating298
Log Tables296
Logarithms to Other Bases Than 10296
The Power ofMathematical Notation295
Powers and Logs ofBase 10295
to Logarithms296
Supersonic and Hypersonic Flight299
Use in Medical Equipment298
Sound Intensity297

Logarithms Designing Radioactive Shielding Estimating the Age ofOrganic Matter Powers and Their Relation Using a Logarithmic Scale to Measure

Boolean Logic300
Fuzzy Logic300
Proposition and Conclusion300
Reasoning300

Logic

Designing Cars305
Digital Images304
Flying the Space Shuttle305
Population Biology305

Matrices and Determinants

Accuracy in Measurement309
Archaeology310
Architecture310
Blood Pressure310
Chemistry310
Computers310
The Definition ofa Second310
Dimensions308
Doctors and Medicine310
Engineering309
and Quality Control309
Gravity313
Distances in Space312
Measuring Distance308
Measuring Mass313
Measuring the Speed ofGravity313
Measuring Time310
Navigation310
Nuclear Power Plants310
Space Travel and Timekeeping312
Speed of Light312

Measurement Evaluating Errors in Measurement How Astronomers and NASA Measure Measuring Speed,Space Travel,and Racing...310

Calculation ofBody Mass Index (BMI)319
Clinical Trials323
Rate ofBacterial Growth326
in Height and Weight Charts319
Value ofDiagnostic Tests318

Medical Mathematics Genetic Risk Factors:the Inheritance ofDisease..321 Standard Deviation and Variance for Use

Ecological Modeling330
Military Modeling331

Modeling

Multiplication

a Baseball ERA338
Calculating Exponential Growth Rates338
Calculating Miles Per Gallon341
Electronic Timing339
Exponents and Growth Rates337

Sports Multiplication:Calculating Investment Calculations .......... 337

Entries (With Areas of Discussion)

Measurement Systems339
Multiplication in International Travel339
Other Uses ofMultiplication340
Rate of Pay339
Savings341
SPAM and Email Communications341

REAL-LIFE MATHxiii

Acoustic Design348
Compressing Music349
Computer-Generated Music349
Digital Music348
Discordance ofthe Spheres346
Electronic Instruments347
Error Correction349
Frequency ofConcert A351
Mathematical Analysis ofSound347
Math-Rock351
Medieval Monks345
Pythagoras and Strings343
Quantification of Music345
Using Randomness349
Well-Tempered Tones346

Music and Mathematics

Fibonacci Numbers and the Golden Ratio353
Mathematical Modeling ofNature354
Using Fractals to Represent Nature355

Nature and Numbers Specify Application Using Alphabetizable Title..355

Accounting Practice357
Buildings359
Flood Control358
The Mathematics ofBookkeeping357
Sports358
Temperature Measurement357

Negative Numbers

Cryptography362
Error Correcting Codes363

Number Theory

Odds in Everyday Life367
Odds in State Lotteries368
Odds, Other Applications369
Sports and Entertainment Odds366

Odds

Calculating a Tip375
Compound Interest376
Definitions and Basic Applications372
Applications374
Finding the Base Rate374
Finding the Original Amount375
Finding the Rate ofIncrease or Decrease375
Finding the Rate Percent374
Important Percentage Applications374
Percentage Change:Increase or Decrease375
Public Opinion Polls379
Ratios, Proportions, and Percentages373
Rebate Period and Cost378
Rebates377
and Sales Tax376

Percentages Examples ofCommon Percentage Retail Sales:Price Discounts and Markups

Versus Mail-In Rebate377
Sales Tax Calculations377
SAT Scores or Other Academic Testing383
Sports Math379
Tournaments and Championships382
Understanding Percentages in the Media378
Using Percentages to Make Comparisons379

Sales Tax Calculation:In-Store Discount

Bodies of Water386
Landscaping386
Military387
Planetary Exploration388
Robotic Perimeter Detection Systems388
Security Systems386
Sporting Events386

Perimeter

Animation392
Art391
Computer Graphics395
Film393
Illustration392
Interior Design394

Entries (With Areas of Discussion)

xivREAL-LIFE MATH

The Camera398
Depth of Field400
Digital Image Processing403
Digital Photography401
Film Speed398
Lens Aperture400
Lens Focal Length399
Photomicrography403
Reciprocity401
Shutter Speed399
Sports and Wildlife Photography402

Photography Math

Area Chart406
Bar Graphs406
Body Diagram414
Box Plot405
Circuit Diagram414
Diagrams404
Fishbone Diagram406
Flow Chart411
Gantt Charts413
Line Graph408
Maps413
Organization Charts413
Other Diagrams414
Pie Graph406
Polar Chart406
Properties of Graphs404
Scatter Graph405
Stem and LeafPlots405
Street Signs414
Three-Dimensional Graph407
Tree Diagram412
Triangular Graph407
Weather Maps414

Plots and Diagrams

Acids,Bases,and pH Level418
of Solid Figures417
Astronomy and Brightness ofStars418
Logic417
Earthquakes and the Richter Scale417
The Powers ofNanotechnology418

Powers Areas ofPolygons and Volumes Computer Science and Binary

Biological Applications ofPrime Numbers421

Prime Numbers

Gambling and Probability Myths425
Probability in Business and Industry427
Probability, Other Uses428
Probability in Sports and Entertainment426
Security424

Probability

Architecture432
Art, Sculpture, and Design432
Chemistry435
Diets436
Direct Proportion431
Engineering Design435
Ergonomics434
Inverse Proportion431
Maps434
Medicine434
Musical Instruments435
Proportion in Nature436
Solving Ratios With Cross Products430
Stock Market436

Proportion

Acceleration439
Area and Volume439
Car Tires439
Guiding Weapons440
Hospital Size440
Just in Time Manufacturing440

Quadratic,Cubic,and Quartic Equations

Age of Earth446
Automobile Performance445
Cleaning Water446
Cooking446
Cost of Gas443
Genetic Traits443
Healthy Living446
Length ofa Trip443

Entries (With Areas of Discussion)

Optimizing Livestock Production447
Sports445
Stem Cell Research446
Student-Teacher Ratio445

REAL-LIFE MATHxv

Accounting451
Bulk Purchases450
Decimals450
Energy Consumption451
Length and Weight450
Lunar Cycles451
Mileage452
Pi450
Population451
Precision452
Time452
Weight Determination451
Whole Numbers449

Rounding

Analytic Rubrics and Holistic Rubrics455
Rubrics455
Scoring Rubrics453

Rubric General Rubrics and Task-Specific

Agriculture459
Archeology463
Astronomy462
Demographic Surveys462
Drug Manufacturing460
Environmental Studies462
Market Assessment463
Marketing463
Non-Probability Sampling458
Plant Analysis460
Probability Sampling457
Scientific Research460
Soil Sampling460
Weather Forecasts461

Sampling

Architecture468
Atmospheric Pressure Using Barometer469
The Calendar469

Scale

to the Universe471
Interval Scale466
Linear Scale465
Logarithmic Scale465
Map Scale467
Measuring Wind Strength469
The Metric System ofMeasurement472
Music471
Nominal Scale467
Ordinal Scale467
Ratio Scale466
The Richter Scale470
Sampling472
Technology and Imaging469
Toys471
Weighing Scale468

Expanse ofScale From the Sub-Atomic

Aviation and Flights478
Bridging Chasms478
Discrete Math474
Earthquakes and Logarithms482
Equations and Graphs476
Functions and Measurements473
Genetics483
Logarithms475
Matrices and Arrays475
Medical Imaging480
Rocket Launch480
Ships482
Simple Carpentry479
Weather Prediction476
Wind Chill in Cold Weather476
Absolute Dating489
Chemistry486
Computer Science487
Cosmology487
Earth Science489
Electrical Circuits486
Electronics489
Engineering487
Environmental Science488
Forensic Science488

Entries (With Areas of Discussion)

xviREAL-LIFE MATH

and Astronomy486
Medicine488
Nanotechnology490
Proteins and Biology490

Light Years,the Speed ofLight,

Genetics493
Operating On Sets492
Ordering Things493
Sequences491
Series492
Sets491
Using Sequences493

Sequences, Sets, and Series

Baseball498
Basketball499
Work505
Football—How Far was the Pass Thrown?507
Decision-Making Tool501
Golf Technology506
Math and the Science ofSport504
Math and Sports Wagering508
Math to Understand Sports Performance497
Mathematics and the Judging ofSports504
Money in Sport—Capology 101507
North American Football499
Ratings Percentage Index (RPI)503
Rules Math496
of the Ball506
Understanding the Sports Media Expert502

Sports Math Cycling—Gear Ratios and How They Football Tactics—Math as a Pascal’s Triangle and Predicting a Coin Toss...500 Predicting the Future:Calling the Coin Toss...500 Soccer—Free Kicks and the Trajectory

Architecture513
Global Economics515
Hiopasus’s Fatal Discovery513
Names and Conventions512
Navigation514
Pythagorean Theorem513
Sports514
Stock Markets515

Square and Cube Roots

Analysis of Variance522
Average Values519
Confidence Intervals522
Correlation and Curve Fitting521
Cumulative Frequencies and Quantiles521
Geostatistics525
Measures of Dispersion520
Minimum, Maximum, and Range518
Populations and Samples516
Probability517
Public Opinion Polls527
Quality Assurance526
Statistical Hypothesis Testing522
Using Statistics to Deceive523

Statistics

Subtraction

and Recreation533
Subtraction in Financial Calculations531
Subtraction in Politics and Industry535
Tax Deductions532

Subtraction in Entertainment

Architecture541
Exploring Symmetries539
Fractal Symmetries541
Imperfect Symmetries542
Symmetries in Nature542

Symmetry

Converting Measurements545
Daily Use549
Educational Tables545
Finance546
Health548
Math Skills544
Travel549

Tables

Computer Networking5
I.Q. Tests5
Möbius Strip5
Visual Analysis554

Entries (With Areas of Discussion)

REAL-LIFE MATHxvii

Chemical Analysis566
Computer Graphics566
Law of Sines561
Measuring Angles557
Navigation562
Pythagorean Theorem559
Surveying, Geodesy, and Mapping564
Trigonometric Functions560
Types of Triangles558
Vectors, Forces, and Velocities563

Trigonometry

3-D Computer Graphics572
Drag Racing572
Land Mine Detection572
The Magnitude ofa Vector569
Sports Injuries573
Three-Dimensional Vectors569
Two-Dimensional Vectors568
Vector Algebra570
Vectors in Linear Algebra571

Vectors

Biometric Measurements581
Building and Architecture579
Compression Ratios in Engines579
Glowing Bubbles: Sonoluminescence579
Medical Applications578
Misleading Graphics581
Pricing577
Runoff582
Sea Level Changes580
Swimming Pool Maintenance581
Units of Volume575
Volume ofa Box575
Volumes ofCommon Solids575
Why Thermometers Work580

Volume

Accounts and VAT592
Archaeology585
Architecture590
Average Height?593
Bearings and Directions ofTravel592
Comparisons586
Computer Programming584
Cooking Instructions591
Creative Design584
Cryptography585
Decorating594
Disease Control591
Ecology587
Efficient Packing and Organization590
Engineering585
Exchange Rates586
Finance591
Geology591
Global Warming594
Graph Theory588
Hypothesis Testing585
Insurance584
Linear Programming588
Lotteries and Gambling591
Measuring Height ofa Well594
Medicine and Cures585
MMR Immunization and Autism594
Navigation587
Opinion Polls593
Percentages586
Phone Companies586
Postman589
Proportion and Inverse Proportion586
Quality Control592
Ranking Test Scores589
Recipes591
ROTA and Timetables589
Searching in an Index590
Seeding in Tournaments590
to a Whole Town589
Software Design584
Stock Keeping592
Store Assistants592
Surveying592
Teachers584
Throwing a Ball593
Translation587
Travel and Racing586
Traveling Salesperson589
Weather593

Word Problems Banks,Interest Rates,and Introductory Rates...591 Shortest Links to Establish Electricity

Currency, Futures, and Stock Markets597
Experimental Gaming597
Gambling596

REAL-LIFE MATHxix

Introduction

Real-Life Mathtakes an international perspective in exploring the role ofmathematics in everyday life and is intended for high school age readers.As Real-Life Math (RLM) is intended for a younger and less mathematically experienced audience,the authors and editors faced unique challenges in selecting and preparing entries.

The articles in the book are meant to be understandable by anyone with a curiosity about mathematical topics. Real-Life Mathis intended to serve all students ofmath such that an 8th- or 9th-grade student just beginning their study ofhigher maths can at least partially comprehend and appreciate the value ofcourses to be taken in future years.Accordingly,articles were constructed to contain material that might serve all students.For example,the article,“Calculus”is intended to be able to serve students taking calculus,students finished with prerequisites and about to undertake their study ofcalculus,and students in basic math or algebra who might have an interest in the practical utility ofa far-offstudy ofcalculus.Readers should anticipate that they might be able to read and reread articles several times over the course oftheir studies in maths.Real-Life Mathchallenges students on multiple levels and is designed to facilitate critical thinking and reading-in-context skills.The beginning student is not expected to understand more mathematically complex text dealing,for example,with the techniques for calculus, and so should be content to skim through these sections as they read about the practical applications.As students progress through math studies,they will naturally appreciate greater portions ofmore advanced sections designed to serve more advanced students.

To be ofmaximum utility to students and teachers, most ofthe 80 topics found herein—arranged alphabetically by theory or principle—were predesigned to correspond to commonly studied fundamental mathematical concepts as stated in high school level curriculum objectives.However,as high school level maths generally teach concepts designed to develop skills toward higher maths ofgreater utility,this format sometimes presented a challenge with regard to articulating understandable or direct practical applications for fundamental skills without introducing additional concepts to be studied in more advanced math classes.It was sometimes difficult to isolate practical applications for fundamental concepts because it often required more complex mathematical concepts to most accurately convey the true relationship ofmathematics to our advancing technology.Both the authors and editors ofthe project made exceptional efforts to smoothly and seamlessly incorporate the concepts necessary (and at an accessible level) within the text.

Although the authors ofReal-Life Mathinclude math teachers and professors,the bulk ofthe writers are

Introduction xxREAL-LIFE MATH practicing engineers and scientists who use math on a daily basis.However,RLMis not intended to be a book about real-life applications as used by mathematicians and scientists but rather,wherever possible,to illustrate and discuss applications within the experience—and that are understandable and interesting—to younger readers.

RLMis intended to maximize readability and accessibility by minimizing the use ofequations,example problems,proofs,etc.Accordingly,RLMis not a math textbook, nor is it designed to fully explain the mathematics involved in each concept.Rather,RLMis intended to compliment the mathematics curriculum by serving a general reader for maths by remaining focused on fundamental math concepts as opposed to the history ofmath,biographies of mathematicians,or simply interesting applications.To be sure,there are inherent difficulties in presenting mathematical concepts without the use ofmathematical notation,but the authors and editors ofRLMsought to use descriptions and concepts instead ofmathematical notation,problems,and proofs whenever possible.

To the extent that RLMmeets these challenges it becomes a valuable resource to students and teachers of mathematics.

The editors modestly hope that Real-Life Mathserves to help students appreciate the scope ofthe importance and influence ofmath on everyday life.RLMwill achieve its highest purposes ifit intrigues and inspires students to continue their studies in maths and so advance their understanding ofthe both the utility and elegance of mathematics.

“[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written.It is written in mathematical language, and the letters are triangles,circles,and other geometrical figures,without which means it is humanly impossible to comprehend a single word.”Galilei,Galileo (1564–1642)

K.Lee Lerner and Brenda Wilmoth Lerner,Editors

REAL-LIFE MATHxxi

List of Advisors and Contributors

In compiling this edition,we have been fortunate in being able to rely upon the expertise and contributions of the following scholars who served as contributing advisors or authors for Real-Life Math,and to them we would like to express our sincere appreciation for their efforts:

William Arthur Atkins

Mr.Atkins holds a BS in physics and mathematics as well as an MBA.He lives atwrites in Perkin,Illinois.

Juli M. Berwald,PhD

In addition to her graduate degree in ocean sciences,Dr.Berwald holds a BA in mathematics from Amherst College,Amherst, Massachusetts.She currently lives and writes in Chicago, Illinois.

Bennett Brooks

Mr.Brooks is a PhD graduate student inmathematics.He holds a BS in mathematics, with departmental honors,from University of Redlands, Redlands, California, and currently works as a writer based in Beaumont, California.

Rory Clarke,PhD

Dr.Clark is a British physicist conducting research in the area ofhigh-energy physics at the University ofBucharest,Romania.He holds a PhD in high energy particle physics from the University ofBirmingham,an MSc in theoretical physics from Imperial College, and a BSc degree in physics from the University of London.

Raymond C. Cole

Mr.Cole is an investment banking financial analyst who lives in New York.He holds anMBA from the Baruch Zicklin School ofBusiness and a BS in business administration from Fordham University.

Bryan Thomas Davies

Mr.Davies holds a Bachelor ofLaws (LLB) from the University ofWestern Ontario and has served as a criminal prosecutor in the Ontario Ministry ofthe Attorney General.In addition to his legal experience,Mr.Davies is a nationally certified basketball coach.

John F. Engle

Mr.Engle is a medical student at Tulane University Medical School in New Orleans, Louisiana.

List of Advisors and Contributors xxiiREAL-LIFE MATH

William J. Engle

Mr.Engle is a retired petroleum engineer who lives in Slidell,Louisiana.

Paul Fellows

Dr.Fellows is a physicist and mathematician who lives in London,England.

Renata A. Ficek

Ms.Ficek is a graduate mathematics student at the University ofQueensland,Australia.

Larry Gilman,PhD

Dr.Gilman holds a PhD in electrical engineering from Dartmouth College andan MA in English literature from Northwestern University.He lives in Sharon,Vermont.

Amit Gupta

Mr.Gupta holds an MS in information systems and is managing director of Agarwal Management Consultants P.Ltd.,in Ahmedabad, India.

William C. Haneberg,PhD

Dr.Haneberg is a professional geologist and writer based in Seattle,Washington.

Bryan D. Hoyle,PhD

Dr.Hoyle is a microbiologist and science writer who lives in Halifax,Nova Scotia, Canada.

Kenneth T. LaPensee,PhD

In addition to professional research in epidemiology, Dr. LaPensee directs Skylands Healthcare Consulting located inHampton, New Jersey.

Holly F. McBain

Ms.McBain is a science and math writer who lives near New Braunfels,Texas.

Mark H. Phillips,PhD

Dr.Phillips serves as an assistant professor ofmanagement at Abilene Christian University, located in Abilene,Texas.

Nephele Tempest

Ms.Tempest is a writer based in Los Angeles, California.

David Tulloch

Mr.Tulloch holds a BSc in physics and an MS in the history ofscience.In addition to research and writing he serves as a radio broadcaster in Ngaio,Wellington,New Zealand.

James A. Yates

Mr.Yates holds a MMath degree from Oxford University and is a teacher ofmaths in Skegnes, England.

The editors would like to extend special thanks to

Connie Clyde for her assistance in copyediting.The editors also wish to especially acknowledge Dr.Larry Gilman for his articles on calculus and exponents as well as his skilled corrections ofthe entire text.The editors are profoundly grateful to their assistant editors and proofreaders,including Lynn Nettles and Bill Engle,who read and corrected articles under the additional pressures created by evacuations mandated by Hurricane Katrina.The final editing of this book was interrupted as Katrina damaged the Gulf Coast homes and offices ofseveral authors,assistant editors,and the editors ofRLMjust as the book was being prepared for press.Quite literally,many pages were read and corrected by light produced by emergency generators— and in some cases,pages were corrected from evacuation shelters.The editors are forever grateful for the patience and kind assistance ofmany fellow scholars and colleagues during this time.

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