**UFRJ**

# 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

Composition Evi Seoud, Mary Beth Trimper

Manufacturing Wendy Blurton, Dorothy Maki

© 2006 Thomson Gale, a part of the Thomson Corporation.

Thomson and Star Logo are trademarks and Gale and UXL are registered trademarks used herein under license.

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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—dc22 | 2005013141 |

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 |

Introduction | xix |

List ofAdvisors and Contributors | xxi |

Entries | 1 |

Addition | 1 |

Algebra | 9 |

Algorithms | 26 |

Architectural Math | 3 |

Area | 45 |

Average | 51 |

Base | 59 |

Business Math | 62 |

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 |

Table of Contents viREAL-LIFE MATH

Matrices and Determinants | 303 |

Measurement | 307 |

Medical Mathematics | 314 |

Modeling | 328 |

Multiplication | 335 |

Music and Mathematics | 343 |

Nature and Numbers | 353 |

Negative Numbers | 356 |

Number Theory | 360 |

Odds | 365 |

Percentages | 372 |

Perimeter | 385 |

Perspective | 389 |

Photography Math | 398 |

Plots and Diagrams | 404 |

Powers | 416 |

Prime Numbers | 420 |

Probability | 423 |

Proportion | 430 |

Quadratic, Cubic, and Quartic Equations | 438 |

Ratio | 441 |

Rounding | 449 |

Rubric | 453 |

Sampling | 457 |

Scale | 465 |

Scientific Math | 473 |

Scientific Notation | 484 |

Sequences, Sets, and Series | 491 |

Sports Math | 495 |

Square and Cube Roots | 511 |

Statistics | 516 |

Subtraction | 529 |

Symmetry | 537 |

Tables | 543 |

Topology | 553 |

Trigonometry | 557 |

Vectors | 568 |

Volume | 575 |

Word Problems | 583 |

Zero-sum Games | 595 |

Glossary | 599 |

Field ofApplication Index | 605 |

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

REAL-LIFE MATHvii

Entries (With Areas of Discussion)

Financial Addition | 4 |

Geometric Progression | 6 |

Sports and Fitness Addition | 3 |

Using Addition to Predict and Entertain | 6 |

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

Art | 21 |

Building Skyscrapers | 19 |

Buying Light Bulbs | 20 |

College Football | 14 |

Crash Tests | 18 |

Fingerprint Scanners | 2 |

Flying an Airplane | 16 |

Fundraising | 19 |

Personal Finances | 13 |

Population Dynamics | 2 |

Private Space Travel | 24 |

Skydiving | 17 |

Teleportation | 23 |

UPC Barcodes | 15 |

Algebra

Archeology | 27 |

Artificial Intelligence | 32 |

Computer Programming | 27 |

Credit Card Fraud Detection | 27 |

Cryptology | 28 |

Data Mining | 28 |

DNA or Genetic Analysis | 28 |

Encryption and Encryption Devices | 28 |

The Genetic Code | 30 |

Imaging | 29 |

Internet Data Transmission | 29 |

Linguistics, the Study of Language | 31 |

Mapping | 30 |

Market or Sales Analysis | 30 |

Operational Algorithms | 27 |

Security Devices | 31 |

Sports Standings and Seedings | 31 |

Tax Returns | 31 |

Algorithms Digital Animation and Digital Model Creation..28

Architectural Concepts in Wheels | 43 |

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

Entries (With Areas of Discussion)

Architecture | 36 |

Astronomy | 43 |

Ergonomics | 41 |

Geometry,Basic Forms and Shapes of | 40 |

Golden Rectangle and Golden Ratio | 38 |

Grids, Use of | 37 |

Jewelry | 41 |

Measurement | 35 |

Proportion | 34 |

Ratio | 3 |

Ratio and Proportion,Use of | 38 |

Scale Drawing | 34 |

Space, Use Of | 37 |

Sports | 38 |

Symmetry | 34 |

Symmetry in City Planning | 41 |

Technology | 41 |

Textile and Fabrics | 43 |

viiiREAL-LIFE MATH

Area ofa Rectangle | 45 |

Areas ofCommon Shapes | 46 |

Areas ofSolid Objects | 46 |

Buying by Area | 47 |

Car Radiators | 48 |

Cloud and Ice Area and Global Warming | 47 |

Drug Dosing | 46 |

Filtering | 47 |

Solar Panels | 49 |

Surveying | 48 |

Units of Area | 45 |

Area

Arithmetic Mean | 51 |

The “Average” Family | 5 |

Average Lifespan | 57 |

Averaging for Accuracy | 5 |

Batting Averages | 53 |

Evolution in Action | 57 |

Geometric Mean | 52 |

Grades | 54 |

How Many Galaxies? | 5 |

Insurance | 57 |

Mean | 52 |

Median | 52 |

Space Shuttle Safety | 56 |

Student Loan Consolidation | 56 |

Weighted Averages in Business | 54 |

Weighted Averages in Grading | 54 |

Average

Base 2 and Computers | 60 |

Base

Accounting | 63 |

Budgets | 63 |

Earnings | 6 |

Interest | 67 |

Payroll | 65 |

Profits | 6 |

Business Math

Bridge Construction | 76 |

Combinatorics | 7 |

Compound Interest | 74 |

Financial Transactions | 73 |

Measurement Calculations | 75 |

Nautical Navigation | 73 |

Random Number Generator | 75 |

Supercomputers | 78 |

Understanding Weather | 7 |

Calculator Math

Applications of Derivatives | 86 |

Derivative | 81 |

Functions | 81 |

Fundamental Theorem ofCalculus | 85 |

Integral | 83 |

Integrals, Applications | 91 |

Maxima and Minima | 85 |

Calculus

Gregorian Calendar | 9 |

Islamic and Chinese Calendars | 9 |

Leap Year | 9 |

Calendars

Coordinate Systems | 103 |

GIS-Based Site Selection | 105 |

GPS Navigation | 105 |

Map Projection | 100 |

Scale | 100 |

Entries (With Areas of Discussion)

REAL-LIFE MATHix

Bar Charts | 109 |

Basic Charts | 107 |

Clustered Column Charts | 110 |

Column and Bar Charts | 109 |

Line Charts | 107 |

Pie Charts | 110 |

Stacked Column Charts | 110 |

Using the Computer to Create Charts | 112 |

X-Y Scatter Graphs | 109 |

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

Algorithms | 115 |

Binary System | 114 |

Bits | 116 |

Bytes | 116 |

Compression | 118 |

Data Transmission | 119 |

Encryption | 120 |

IP Address | 117 |

Pixels, Screen Size, and Resolution | 117 |

Subnet Mask | 118 |

Text Code | 116 |

Computers and Mathematics

Absolute Systems | 127 |

Arbitrary Systems | 128 |

Cooking or Baking Temperatures | 127 |

Derived Units | 124 |

English System | 123 |

International System ofUnits (SI) | 123 |

Metric Units | 123 |

Phenomena | 124 |

Weather Forecasting | 126 |

Conversions Units Based On Physical or “Natural”

3-D Systems On Ordinance Survey Maps | 136 |

Cartesian Coordinate Plane | 132 |

Changing Between Coordinate Systems | 132 |

Choosing the Best Coordinate System | 132 |

Commercial Aviation | 135 |

Coordinate Systems Used in Board Games | 134 |

Animation | 134 |

Dimensions ofa Coordinate System | 131 |

Longitude and John Harrison | 135 |

Modern Navigation and GPS | 135 |

Paper Maps ofthe World | 134 |

Polar Coordinates | 133 |

Radar Systems and Polar Coordinates | 136 |

Vectors | 132 |

Coordinate Systems Coordinate Systems Used for Computer

Grade Point Average Calculations | 139 |

Measurement Systems | 139 |

Science | 139 |

Decimals

Census | 142 |

Election Analysis | 141 |

Demographics Geographic Information System Technology...143

Algorithms | 145 |

Boolean Algebra | 145 |

Combinatorial Chemistry | 147 |

Combinatorics | 145 |

Computer Design | 146 |

Cryptography | 146 |

Finding New Drugs with Graph Theory | 147 |

Graphs | 146 |

Logic, Sets, and Functions | 144 |

Looking Inside the Body With Matrices | 147 |

Matrix Algebra | 146 |

Number Theory | 145 |

Probability Theory | 145 |

Searching the Web | 146 |

Shopping Online and Prime Numbers | 147 |

Averages | 152 |

Division and Comparison | 151 |

Division and Distribution | 150 |

Division, Other Uses | 153 |

Practical Uses ofDivision For Students | 153 |

Division

Astronomers | 157 |

Entries (With Areas of Discussion)

Computer Control and Coordination | 157 |

Computer Science | 158 |

Engineering | 157 |

Graphs, Charts, Maps | 158 |

Physics | 157 |

xREAL-LIFE MATH

The Age ofthe Universe | 160 |

Conformal Maps | 159 |

E-Money | 160 |

Elliptic Functions

Buying a Used Car | 162 |

Carbon Dating | 165 |

Digital Imaging | 164 |

Gumball Contest | 163 |

Hubble Space Telescope | 165 |

Population Sampling | 164 |

Software Development | 166 |

Estimation

Bases and Exponents | 167 |

Exponents Body Proportions and Growth

Skinny Legs) | 179 |

Credit Card Meltdown | 178 |

Expanding Universe | 178 |

Exponential Functions | 168 |

Exponential Growth | 171 |

Exponents and Evolution | 174 |

Integer Exponents | 167 |

Interest and Inflation | 177 |

Non-Integer Exponents | 168 |

Radioactive Dating | 177 |

Radioactive Decay | 175 |

Rotting Leftovers | 173 |

Scientific Notation | 171 |

(Why Elephants Don’t Have

Codes and Code Breaking | 182 |

Distribution | 182 |

Geometry and Approximation ofSize | 182 |

and Behaviors | 181 |

Reducing Equations | 181 |

Skill Transfer | 182 |

Factoring Identification ofPatterns

Balancing a Checkbook | 189 |

Budgets | 188 |

Buying Music | 184 |

Calculating a Tip | 194 |

Car Purchasing and Payments | 187 |

Choosing a Wireless Plan | 187 |

Credit Cards | 185 |

Currency Exchange | 195 |

Investing | 190 |

Retirement Investing | 192 |

Social Security System | 190 |

Understanding Income Taxes | 189 |

Financial Calculations, Personal

Astronomy | 202 |

Building Fractals | 199 |

Cell Phone and Radio Antenna | 202 |

Computer Science | 202 |

Fractals and Nature | 200 |

Modeling Hurricanes and Tornadoes | 201 |

Nonliving Systems | 201 |

Similarity | 199 |

Fractals

Algebra | 205 |

Cooking and Baking | 206 |

Fractions and Decimals | 204 |

Fractions and Percentages | 204 |

Fractions and Voting | 208 |

Music | 206 |

Overtime Pay | 208 |

Radioactive Waste | 206 |

Rules For Handling Fractions | 204 |

Simple Probabilities | 207 |

Tools and Construction | 208 |

Types of Fractions | 203 |

What Is a Fraction? | 203 |

Fractions

Body Mass Index | 214 |

Finite-Element Models | 212 |

Functions, Described | 210 |

Functions and Relations | 210 |

Guilloché Patterns | 211 |

Entries (With Areas of Discussion)

The Million-Dollar Hypothesis | 212 |

Nuclear Waste | 213 |

Synths and Drums | 213 |

REAL-LIFE MATHxi

Basic Board Games | 220 |

Card Games | 218 |

Magic Squares | 221 |

Math Puzzles | 223 |

Other Casino Games | 219 |

Game Math

Artificial Intelligence | 230 |

Decision Theory | 228 |

eBay and the Online Auction World | 230 |

Economics | 229 |

Economics and Game Theory | 228 |

Evolution and Animal Behavior | 229 |

General Equilibrium | 229 |

Infectious Disease Therapy | 230 |

Nash Equilibrium | 229 |

Game Theory

Architecture | 237 |

Fireworks | 241 |

Fourth Dimension | 245 |

Global Positioning | 239 |

Honeycombs | 239 |

Manipulating Sound | 241 |

Pothole Covers | 236 |

Robotic Surgery | 245 |

Rubik’s Cube | 243 |

Shooting an Arrow | 244 |

Solar Systems | 242 |

Stealth Technology | 244 |

Geometry

Aerodynamics and Hydrodynamics | 259 |

Area Graphs | 252 |

Bar Graphs | 249 |

Biomedical Research | 258 |

Bubble Graphs | 257 |

Computer Network Design | 259 |

Finding Oil | 258 |

Gantt Graphs | 254 |

Global Warming | 257 |

GPS Surveying | 258 |

Line Graphs | 251 |

Physical Fitness | 259 |

Picture Graphs | 254 |

Pie Graphs | 252 |

Radar Graphs | 253 |

X-Y Graphs | 254 |

Graphing

Altering Images | 263 |

Analyzing Images | 263 |

Art | 267 |

Compression | 264 |

Creating Images | 263 |

Dance | 266 |

Forensic Digital Imaging | 266 |

Meat and Potatoes | 266 |

Medical Imaging | 264 |

Optics | 264 |

Biometrics Application | 264 |

Steganography and Digital Watermarks | 266 |

Imaging Recognizing Faces:a Controversial

Communications | 273 |

Error Correction | 275 |

Information and Meaning | 273 |

Quantum Computing | 276 |

Unequally Likely Messages | 271 |

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

Anti-Sound | 282 |

On the Eye | 281 |

Cryptography | 280 |

Definition ofan Inverse | 278 |

Fluid Mechanics and Nonlinear Design | 281 |

Inverse Functions | 279 |

The Multiplicative Inverse | 278 |

Negatives Used in Photography | 281 |

Not Exist | 279 |

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

Inverse | 279 |

Stealth Submarine Communications | 282 |

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

Entries (With Areas of Discussion) xiiREAL-LIFE MATH

Iteration and Business | 285 |

Iteration and Computers | 286 |

Iteration and Creativity | 285 |

Iteration and Sports | 284 |

Iteration

Earthquake Prediction | 289 |

Linear Programming | 291 |

Linear Reproduction ofMusic | 292 |

Recovering Human Motion From Video | 290 |

Virtual Tennis | 291 |

Linear Mathematics

Algebra ofPowers ofLogarithms | 296 |

Computer Intensive Applications | 297 |

Cryptography and Group Theory | 299 |

for Equipment in Space | 299 |

Developing Optical Equipment | 298 |

Using Carbon Dating | 298 |

Log Tables | 296 |

Logarithms to Other Bases Than 10 | 296 |

The Power ofMathematical Notation | 295 |

Powers and Logs ofBase 10 | 295 |

to Logarithms | 296 |

Supersonic and Hypersonic Flight | 299 |

Use in Medical Equipment | 298 |

Sound Intensity | 297 |

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

Boolean Logic | 300 |

Fuzzy Logic | 300 |

Proposition and Conclusion | 300 |

Reasoning | 300 |

Logic

Designing Cars | 305 |

Digital Images | 304 |

Flying the Space Shuttle | 305 |

Population Biology | 305 |

Matrices and Determinants

Accuracy in Measurement | 309 |

Archaeology | 310 |

Architecture | 310 |

Blood Pressure | 310 |

Chemistry | 310 |

Computers | 310 |

The Definition ofa Second | 310 |

Dimensions | 308 |

Doctors and Medicine | 310 |

Engineering | 309 |

and Quality Control | 309 |

Gravity | 313 |

Distances in Space | 312 |

Measuring Distance | 308 |

Measuring Mass | 313 |

Measuring the Speed ofGravity | 313 |

Measuring Time | 310 |

Navigation | 310 |

Nuclear Power Plants | 310 |

Space Travel and Timekeeping | 312 |

Speed of Light | 312 |

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

Calculation ofBody Mass Index (BMI) | 319 |

Clinical Trials | 323 |

Rate ofBacterial Growth | 326 |

in Height and Weight Charts | 319 |

Value ofDiagnostic Tests | 318 |

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

Ecological Modeling | 330 |

Military Modeling | 331 |

Modeling

Multiplication

a Baseball ERA | 338 |

Calculating Exponential Growth Rates | 338 |

Calculating Miles Per Gallon | 341 |

Electronic Timing | 339 |

Exponents and Growth Rates | 337 |

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

Entries (With Areas of Discussion)

Measurement Systems | 339 |

Multiplication in International Travel | 339 |

Other Uses ofMultiplication | 340 |

Rate of Pay | 339 |

Savings | 341 |

SPAM and Email Communications | 341 |

REAL-LIFE MATHxiii

Acoustic Design | 348 |

Compressing Music | 349 |

Computer-Generated Music | 349 |

Digital Music | 348 |

Discordance ofthe Spheres | 346 |

Electronic Instruments | 347 |

Error Correction | 349 |

Frequency ofConcert A | 351 |

Mathematical Analysis ofSound | 347 |

Math-Rock | 351 |

Medieval Monks | 345 |

Pythagoras and Strings | 343 |

Quantification of Music | 345 |

Using Randomness | 349 |

Well-Tempered Tones | 346 |

Music and Mathematics

Fibonacci Numbers and the Golden Ratio | 353 |

Mathematical Modeling ofNature | 354 |

Using Fractals to Represent Nature | 355 |

Nature and Numbers Specify Application Using Alphabetizable Title..355

Accounting Practice | 357 |

Buildings | 359 |

Flood Control | 358 |

The Mathematics ofBookkeeping | 357 |

Sports | 358 |

Temperature Measurement | 357 |

Negative Numbers

Cryptography | 362 |

Error Correcting Codes | 363 |

Number Theory

Odds in Everyday Life | 367 |

Odds in State Lotteries | 368 |

Odds, Other Applications | 369 |

Sports and Entertainment Odds | 366 |

Odds

Calculating a Tip | 375 |

Compound Interest | 376 |

Definitions and Basic Applications | 372 |

Applications | 374 |

Finding the Base Rate | 374 |

Finding the Original Amount | 375 |

Finding the Rate ofIncrease or Decrease | 375 |

Finding the Rate Percent | 374 |

Important Percentage Applications | 374 |

Percentage Change:Increase or Decrease | 375 |

Public Opinion Polls | 379 |

Ratios, Proportions, and Percentages | 373 |

Rebate Period and Cost | 378 |

Rebates | 377 |

and Sales Tax | 376 |

Percentages Examples ofCommon Percentage Retail Sales:Price Discounts and Markups

Versus Mail-In Rebate | 377 |

Sales Tax Calculations | 377 |

SAT Scores or Other Academic Testing | 383 |

Sports Math | 379 |

Tournaments and Championships | 382 |

Understanding Percentages in the Media | 378 |

Using Percentages to Make Comparisons | 379 |

Sales Tax Calculation:In-Store Discount

Bodies of Water | 386 |

Landscaping | 386 |

Military | 387 |

Planetary Exploration | 388 |

Robotic Perimeter Detection Systems | 388 |

Security Systems | 386 |

Sporting Events | 386 |

Perimeter

Animation | 392 |

Art | 391 |

Computer Graphics | 395 |

Film | 393 |

Illustration | 392 |

Interior Design | 394 |

Entries (With Areas of Discussion)

xivREAL-LIFE MATH

The Camera | 398 |

Depth of Field | 400 |

Digital Image Processing | 403 |

Digital Photography | 401 |

Film Speed | 398 |

Lens Aperture | 400 |

Lens Focal Length | 399 |

Photomicrography | 403 |

Reciprocity | 401 |

Shutter Speed | 399 |

Sports and Wildlife Photography | 402 |

Photography Math

Area Chart | 406 |

Bar Graphs | 406 |

Body Diagram | 414 |

Box Plot | 405 |

Circuit Diagram | 414 |

Diagrams | 404 |

Fishbone Diagram | 406 |

Flow Chart | 411 |

Gantt Charts | 413 |

Line Graph | 408 |

Maps | 413 |

Organization Charts | 413 |

Other Diagrams | 414 |

Pie Graph | 406 |

Polar Chart | 406 |

Properties of Graphs | 404 |

Scatter Graph | 405 |

Stem and LeafPlots | 405 |

Street Signs | 414 |

Three-Dimensional Graph | 407 |

Tree Diagram | 412 |

Triangular Graph | 407 |

Weather Maps | 414 |

Plots and Diagrams

Acids,Bases,and pH Level | 418 |

of Solid Figures | 417 |

Astronomy and Brightness ofStars | 418 |

Logic | 417 |

Earthquakes and the Richter Scale | 417 |

The Powers ofNanotechnology | 418 |

Powers Areas ofPolygons and Volumes Computer Science and Binary

Biological Applications ofPrime Numbers | 421 |

Prime Numbers

Gambling and Probability Myths | 425 |

Probability in Business and Industry | 427 |

Probability, Other Uses | 428 |

Probability in Sports and Entertainment | 426 |

Security | 424 |

Probability

Architecture | 432 |

Art, Sculpture, and Design | 432 |

Chemistry | 435 |

Diets | 436 |

Direct Proportion | 431 |

Engineering Design | 435 |

Ergonomics | 434 |

Inverse Proportion | 431 |

Maps | 434 |

Medicine | 434 |

Musical Instruments | 435 |

Proportion in Nature | 436 |

Solving Ratios With Cross Products | 430 |

Stock Market | 436 |

Proportion

Acceleration | 439 |

Area and Volume | 439 |

Car Tires | 439 |

Guiding Weapons | 440 |

Hospital Size | 440 |

Just in Time Manufacturing | 440 |

Quadratic,Cubic,and Quartic Equations

Age of Earth | 446 |

Automobile Performance | 445 |

Cleaning Water | 446 |

Cooking | 446 |

Cost of Gas | 443 |

Genetic Traits | 443 |

Healthy Living | 446 |

Length ofa Trip | 443 |

Entries (With Areas of Discussion)

Optimizing Livestock Production | 447 |

Sports | 445 |

Stem Cell Research | 446 |

Student-Teacher Ratio | 445 |

REAL-LIFE MATHxv

Accounting | 451 |

Bulk Purchases | 450 |

Decimals | 450 |

Energy Consumption | 451 |

Length and Weight | 450 |

Lunar Cycles | 451 |

Mileage | 452 |

Pi | 450 |

Population | 451 |

Precision | 452 |

Time | 452 |

Weight Determination | 451 |

Whole Numbers | 449 |

Rounding

Analytic Rubrics and Holistic Rubrics | 455 |

Rubrics | 455 |

Scoring Rubrics | 453 |

Rubric General Rubrics and Task-Specific

Agriculture | 459 |

Archeology | 463 |

Astronomy | 462 |

Demographic Surveys | 462 |

Drug Manufacturing | 460 |

Environmental Studies | 462 |

Market Assessment | 463 |

Marketing | 463 |

Non-Probability Sampling | 458 |

Plant Analysis | 460 |

Probability Sampling | 457 |

Scientific Research | 460 |

Soil Sampling | 460 |

Weather Forecasts | 461 |

Sampling

Architecture | 468 |

Atmospheric Pressure Using Barometer | 469 |

The Calendar | 469 |

Scale

to the Universe | 471 |

Interval Scale | 466 |

Linear Scale | 465 |

Logarithmic Scale | 465 |

Map Scale | 467 |

Measuring Wind Strength | 469 |

The Metric System ofMeasurement | 472 |

Music | 471 |

Nominal Scale | 467 |

Ordinal Scale | 467 |

Ratio Scale | 466 |

The Richter Scale | 470 |

Sampling | 472 |

Technology and Imaging | 469 |

Toys | 471 |

Weighing Scale | 468 |

Expanse ofScale From the Sub-Atomic

Aviation and Flights | 478 |

Bridging Chasms | 478 |

Discrete Math | 474 |

Earthquakes and Logarithms | 482 |

Equations and Graphs | 476 |

Functions and Measurements | 473 |

Genetics | 483 |

Logarithms | 475 |

Matrices and Arrays | 475 |

Medical Imaging | 480 |

Rocket Launch | 480 |

Ships | 482 |

Simple Carpentry | 479 |

Weather Prediction | 476 |

Wind Chill in Cold Weather | 476 |

Absolute Dating | 489 |

Chemistry | 486 |

Computer Science | 487 |

Cosmology | 487 |

Earth Science | 489 |

Electrical Circuits | 486 |

Electronics | 489 |

Engineering | 487 |

Environmental Science | 488 |

Forensic Science | 488 |

Entries (With Areas of Discussion)

xviREAL-LIFE MATH

and Astronomy | 486 |

Medicine | 488 |

Nanotechnology | 490 |

Proteins and Biology | 490 |

Light Years,the Speed ofLight,

Genetics | 493 |

Operating On Sets | 492 |

Ordering Things | 493 |

Sequences | 491 |

Series | 492 |

Sets | 491 |

Using Sequences | 493 |

Sequences, Sets, and Series

Baseball | 498 |

Basketball | 499 |

Work | 505 |

Football—How Far was the Pass Thrown? | 507 |

Decision-Making Tool | 501 |

Golf Technology | 506 |

Math and the Science ofSport | 504 |

Math and Sports Wagering | 508 |

Math to Understand Sports Performance | 497 |

Mathematics and the Judging ofSports | 504 |

Money in Sport—Capology 101 | 507 |

North American Football | 499 |

Ratings Percentage Index (RPI) | 503 |

Rules Math | 496 |

of the Ball | 506 |

Understanding the Sports Media Expert | 502 |

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

Architecture | 513 |

Global Economics | 515 |

Hiopasus’s Fatal Discovery | 513 |

Names and Conventions | 512 |

Navigation | 514 |

Pythagorean Theorem | 513 |

Sports | 514 |

Stock Markets | 515 |

Square and Cube Roots

Analysis of Variance | 522 |

Average Values | 519 |

Confidence Intervals | 522 |

Correlation and Curve Fitting | 521 |

Cumulative Frequencies and Quantiles | 521 |

Geostatistics | 525 |

Measures of Dispersion | 520 |

Minimum, Maximum, and Range | 518 |

Populations and Samples | 516 |

Probability | 517 |

Public Opinion Polls | 527 |

Quality Assurance | 526 |

Statistical Hypothesis Testing | 522 |

Using Statistics to Deceive | 523 |

Statistics

Subtraction

and Recreation | 533 |

Subtraction in Financial Calculations | 531 |

Subtraction in Politics and Industry | 535 |

Tax Deductions | 532 |

Subtraction in Entertainment

Architecture | 541 |

Exploring Symmetries | 539 |

Fractal Symmetries | 541 |

Imperfect Symmetries | 542 |

Symmetries in Nature | 542 |

Symmetry

Converting Measurements | 545 |

Daily Use | 549 |

Educational Tables | 545 |

Finance | 546 |

Health | 548 |

Math Skills | 544 |

Travel | 549 |

Tables

Computer Networking | 5 |

I.Q. Tests | 5 |

Möbius Strip | 5 |

Visual Analysis | 554 |

Entries (With Areas of Discussion)

REAL-LIFE MATHxvii

Chemical Analysis | 566 |

Computer Graphics | 566 |

Law of Sines | 561 |

Measuring Angles | 557 |

Navigation | 562 |

Pythagorean Theorem | 559 |

Surveying, Geodesy, and Mapping | 564 |

Trigonometric Functions | 560 |

Types of Triangles | 558 |

Vectors, Forces, and Velocities | 563 |

Trigonometry

3-D Computer Graphics | 572 |

Drag Racing | 572 |

Land Mine Detection | 572 |

The Magnitude ofa Vector | 569 |

Sports Injuries | 573 |

Three-Dimensional Vectors | 569 |

Two-Dimensional Vectors | 568 |

Vector Algebra | 570 |

Vectors in Linear Algebra | 571 |

Vectors

Biometric Measurements | 581 |

Building and Architecture | 579 |

Compression Ratios in Engines | 579 |

Glowing Bubbles: Sonoluminescence | 579 |

Medical Applications | 578 |

Misleading Graphics | 581 |

Pricing | 577 |

Runoff | 582 |

Sea Level Changes | 580 |

Swimming Pool Maintenance | 581 |

Units of Volume | 575 |

Volume ofa Box | 575 |

Volumes ofCommon Solids | 575 |

Why Thermometers Work | 580 |

Volume

Accounts and VAT | 592 |

Archaeology | 585 |

Architecture | 590 |

Average Height? | 593 |

Bearings and Directions ofTravel | 592 |

Comparisons | 586 |

Computer Programming | 584 |

Cooking Instructions | 591 |

Creative Design | 584 |

Cryptography | 585 |

Decorating | 594 |

Disease Control | 591 |

Ecology | 587 |

Efficient Packing and Organization | 590 |

Engineering | 585 |

Exchange Rates | 586 |

Finance | 591 |

Geology | 591 |

Global Warming | 594 |

Graph Theory | 588 |

Hypothesis Testing | 585 |

Insurance | 584 |

Linear Programming | 588 |

Lotteries and Gambling | 591 |

Measuring Height ofa Well | 594 |

Medicine and Cures | 585 |

MMR Immunization and Autism | 594 |

Navigation | 587 |

Opinion Polls | 593 |

Percentages | 586 |

Phone Companies | 586 |

Postman | 589 |

Proportion and Inverse Proportion | 586 |

Quality Control | 592 |

Ranking Test Scores | 589 |

Recipes | 591 |

ROTA and Timetables | 589 |

Searching in an Index | 590 |

Seeding in Tournaments | 590 |

to a Whole Town | 589 |

Software Design | 584 |

Stock Keeping | 592 |

Store Assistants | 592 |

Surveying | 592 |

Teachers | 584 |

Throwing a Ball | 593 |

Translation | 587 |

Travel and Racing | 586 |

Traveling Salesperson | 589 |

Weather | 593 |

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

Currency, Futures, and Stock Markets | 597 |

Experimental Gaming | 597 |

Gambling | 596 |

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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