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Entries (With Areas of Discussion)AdditionFinancial Addition ............ 4 Geometric Progression .......... 6 Poker, Probability, and Other Uses of Addition .. 5 Sports and Fitness Addition ......... 3 Using Addition to Predict and Entertain .... 6 AlgebraArt ................. 21 Building Skyscrapers ........... 19 Buying Light Bulbs ........... 20 College Football ............ 14 Crash Tests .............. 18 Fingerprint Scanners ........... 22 Flying an Airplane ............ 16 Fundraising .............. 19 Personal Finances ............ 13 Population Dynamics ........... 22 Private Space Travel ........... 24 Skydiving ............... 17 Teleportation .............. 23 UPC Barcodes ............. 15 AlgorithmsArcheology .............. 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 of Language ...... 31 Mapping ............... 30 Market or Sales Analysis .......... 30 Operational Algorithms .......... 27 Security Devices ............ 31 Sports Standings and Seedings ........ 31 Tax Returns .............. 31 Architectural MathArchitectural Concepts in Wheels ....... 43 Architectural Symmetry in Buildings ..... 38 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 ................ 33 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 AreaArea of a Rectangle ........... 45 Areas of Common Shapes ......... 46 Areas of Solid 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 AverageArithmetic Mean ............ 51 The "Average" Family ........... 55 Average Lifespan ............ 57 Averaging for Accuracy .......... 55 Batting Averages ............ 53 Evolution in Action ........... 57 Geometric Mean ............ 52 Grades ................ 54 How Many Galaxies? ........... 55 Insurance ............... 57 Mean ................ 52 Median ............... 52 Space Shuttle Safety ........... 56 Student Loan Consolidation ........ 56 Weighted Averages in Business ........ 54 Weighted Averages in Grading ........ 54 BaseBase 2 and Computers .......... 60 Business MathAccounting .............. 63 Budgets ............... 63 Earnings ............... 66 Interest ............... 67 Payroll ................ 65 Profits ................ 66 Calculator MathBridge Construction ........... 76 Combinatorics ............. 77 Compound Interest ........... 74 Financial Transactions .......... 73 Measurement Calculations ......... 75 Nautical Navigation ........... 73 Random Number Generator ........ 75 Supercomputers ............ 78 Understanding Weather .......... 77 CalculusApplications of Derivatives ......... 86 Derivative .............. 81 Functions .............. 81 Fundamental Theorem of Calculus ...... 85 Integral ............... 83 Integrals, Applications .......... 91 Maxima and Minima ........... 85 CalendarsGregorian Calendar ........... 99 Islamic and Chinese Calendars ........ 99 Leap Year ............... 99 CartographyCoordinate Systems ........... 103 GIS-Based Site Selection .......... 105 GPS Navigation ............. 105 Map Projection ............. 100 Natural Resources Evaluation and Protection ... 105 Scale ................ 100 Topographic Maps ............ 104 ChartsBar Charts .............. 109 Basic Charts .............. 107 Choosing the Right Type of Chart For the Data .. 112 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 Computers and MathematicsAlgorithms .............. 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 ConversionsAbsolute Systems ............ 127 Arbitrary Systems ............ 128 Cooking or Baking Temperatures ....... 127 Derived Units ............. 124 English System ............. 123 International System of Units (SI) ...... 123 Metric Units .............. 123 Units Based On Physical or "Natural" Phenomena ............ 124 Weather Forecasting ........... 126 Coordinate Systems3-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 Coordinate Systems Used for Computer Animation ............. 134 Dimensions of a Coordinate System ...... 131 Longitude and John Harrison ........ 135 Modern Navigation and GPS ........ 135 Paper Maps of the World ......... 134 Polar Coordinates ............ 133 Radar Systems and Polar Coordinates ..... 136 Vectors ............... 132 DecimalsGrade Point Average Calculations ....... 139 Measurement Systems .......... 139 Science ............... 139 DemographicsCensus ............... 142 Election Analysis ............ 141 Geographic Information System Technology ... 143 Discrete MathematicsAlgorithms ............. 145 Boolean Algebra ............ 145 Combinatorial Chemistry ......... 147 Combinatorics ............. 145 Computer Design ............ 146 Counting Jaguars Using Probability Theory ... 147 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 DivisionAverages ............... 152 Division and Comparison ......... 151 Division and Distribution ......... 150 Division, Other Uses ........... 153 Practical Uses of Division For Students ..... 153 Domain and RangeAstronomers ............. 157 Calculating Odds and Outcomes ....... 157 Computer Control and Coordination ..... 157 Computer Science ............ 158 Engineering .............. 157 Graphs, Charts, Maps ........... 158 Physics ............... 157 Elliptic FunctionsThe Age of the Universe .......... 160 Conformal Maps ............ 159 E-Money ............... 160 EstimationBuying a Used Car ............ 162 Carbon Dating ............. 165 Digital Imaging ............. 164 Gumball Contest ............ 163 Hubble Space Telescope .......... 165 Population Sampling ........... 164 Software Development .......... 166 ExponentsBases and Exponents ........... 167 Body Proportions and Growth (Why Elephants Don't Have 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 FactoringCodes and Code Breaking ......... 182 Distribution .............. 182 Geometry and Approximation of Size ..... 182 Identification of Patterns and Behaviors ........... 181 Reducing Equations ........... 181 Skill Transfer ............. 182 Financial Calculations, PersonalBalancing 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 FractalsAstronomy .............. 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 FractionsAlgebra ............... 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 FunctionsBody Mass Index ............ 214 Finite-Element Models .......... 212 Functions, Described ........... 210 Functions and Relations .......... 210 Guilloché Patterns ........... 211 Making Airplanes Fly ........... 211 The Million-Dollar Hypothesis ....... 212 Nuclear Waste ............. 213 Synths and Drums ............ 213 Game MathBasic Board Games ............ 220 Card Games .............. 218 Magic Squares ............. 221 Math Puzzles ............. 223 Other Casino Games ........... 219 Game TheoryArtificial 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 GeometryArchitecture .............. 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 GraphingAerodynamics 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 ImagingAltering 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 Recognizing Faces: a Controversial Biometrics Application ......... 264 Steganography and Digital Watermarks ..... 266 Information TheoryCommunications ............ 273 Error Correction ............ 275 Information and Meaning ......... 273 Information Theory in Biology and Genetics ... 274 Quantum Computing .......... 276 Unequally Likely Messages ......... 271 InverseAnti-Sound .............. 282 The Brain and the Inverted Image On the Eye ............. 281 Cryptography ............. 280 Definition of an Inverse .......... 278 Fluid Mechanics and Nonlinear Design ..... 281 Inverse Functions ............ 279 The Multiplicative Inverse ......... 278 Negatives Used in Photography ....... 281 Operations Where the Inverse Does Not Exist ............. 279 Operations With More Than One Inverse .............. 279 Stealth Submarine Communications ...... 282 Stereo ................ 282 IterationIteration and Business .......... 285 Iteration and Computers ......... 286 Iteration and Creativity .......... 285 Iteration and Sports ........... 284 Linear MathematicsEarthquake Prediction .......... 289 Linear Programming ........... 291 Linear Reproduction of Music ........ 292 Recovering Human Motion From Video .... 290 Virtual Tennis ............. 291 LogarithmsAlgebra of Powers of Logarithms ....... 296 Computer Intensive Applications ....... 297 Cryptography and Group Theory ....... 299 Designing Radioactive Shielding for Equipment in Space ........ 299 Developing Optical Equipment ........ 298 Estimating the Age of Organic Matter Using Carbon Dating ......... 298 Log Tables .............. 296 Logarithms to Other Bases Than 10 ...... 296 The Power of Mathematical Notation ..... 295 Powers and Logs of Base 10 ......... 295 Powers and Their Relation to Logarithms ............ 296 Supersonic and Hypersonic Flight ...... 299 Use in Medical Equipment ......... 298 Using a Logarithmic Scale to Measure Sound Intensity ........... 297 LogicBoolean Logic ............. 300 Fuzzy Logic .............. 300 Proposition and Conclusion ........ 300 Reasoning .............. 300 Matrices and DeterminantsDesigning Cars ............. 305 Digital Images ............. 304 Flying the Space Shuttle .......... 305 Population Biology ........... 305 MeasurementAccuracy in Measurement ......... 309 Archaeology .............. 310 Architecture .............. 310 Blood Pressure ............. 310 Chemistry .............. 310 Computers .............. 310 The Definition of a Second ......... 310 Dimensions .............. 308 Doctors and Medicine ........... 310 Engineering .............. 309 Evaluating Errors in Measurement and Quality Control ......... 309 Gravity ............... 313 How Astronomers and NASA Measure Distances in Space .......... 312 Measuring Distance ........... 308 Measuring Mass ............ 313 Measuring the Speed of Gravity ....... 313 Measuring Speed, Space Travel, and Racing ... 310 Measuring Time ............ 310 Navigation .............. 310 Nuclear Power Plants ........... 310 Space Travel and Timekeeping ........ 312 Speed of Light ............. 312 Medical MathematicsCalculation of Body Mass Index (BMI) ..... 319 Clinical Trials ............. 323 Genetic Risk Factors: the Inheritance of Disease .. 321 Rate of Bacterial Growth ......... 326 Standard Deviation and Variance for Use in Height and Weight Charts ...... 319 Value of Diagnostic Tests ......... 318 ModelingEcological Modeling ........... 330 Military Modeling ............ 331 MultiplicationSports Multiplication: Calculating a Baseball ERA ........... 338 Calculating Exponential Growth Rates ..... 338 Calculating Miles Per Gallon ........ 341 Electronic Timing ............ 339 Exponents and Growth Rates ........ 337 Investment Calculations .......... 337 Measurement Systems .......... 339 Multiplication in International Travel ..... 339 Other Uses of Multiplication ........ 340 Rate of Pay .............. 339 Savings ............... 341 SPAM and Email Communications ...... 341 Music and MathematicsAcoustic Design ............ 348 Compressing Music ........... 349 Computer-Generated Music ........ 349 Digital Music .............. 348 Discordance of the Spheres ......... 346 Electronic Instruments .......... 347 Error Correction ............ 349 Frequency of Concert A .......... 351 Mathematical Analysis of Sound ....... 347 Math-Rock .............. 351 Medieval Monks ............ 345 Pythagoras and Strings .......... 343 Quantification of Music .......... 345 Using Randomness ........... 349 Well-Tempered Tones ........... 346 Nature and NumbersFibonacci Numbers and the Golden Ratio .... 353 Mathematical Modeling of Nature ...... 354 Specify Application Using Alphabetizable Title .. 355 Using Fractals to Represent Nature ...... 355 Negative NumbersAccounting Practice ........... 357 Buildings ............... 359 Flood Control ............. 358 The Mathematics of Bookkeeping ...... 357 Sports ................ 358 Temperature Measurement ......... 357 Number TheoryCryptography ............. 362 Error Correcting Codes .......... 363 OddsOdds in Everyday Life .......... 367 Odds in State Lotteries .......... 368 Odds, Other Applications ......... 369 Sports and Entertainment Odds ....... 366 PercentagesCalculating a Tip ............ 375 Compound Interest ........... 376 Definitions and Basic Applications ...... 372 Examples of Common Percentage Applications ............ 374 Finding the Base Rate ........... 374 Finding the Original Amount ........ 375 Finding the Rate of Increase 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 Retail Sales: Price Discounts and Markups and Sales Tax ............ 376 Sales Tax Calculation: In-Store Discount 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 PerimeterBodies of Water ............. 386 Landscaping .............. 386 Military ............... 387 Planetary Exploration ........... 388 Robotic Perimeter Detection Systems ..... 388 Security Systems ............ 386 Sporting Events ............ 386 PerspectiveAnimation .............. 392 Art ................. 391 Computer Graphics ........... 395 Film ................ 393 Illustration .............. 392 Interior Design ............. 394 Landscaping .............. 395 Photography MathThe 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 Plots and DiagramsArea 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 Leaf Plots ........... 405 Street Signs .............. 414 Three-Dimensional Graph ......... 407 Tree Diagram ............. 412 Triangular Graph ............ 407 Weather Maps ............. 414 PowersAcids, Bases, and pH Level ......... 418 Areas of Polygons and Volumes of Solid Figures ........... 417 Astronomy and Brightness of Stars ...... 418 Computer Science and Binary Logic .............. 417 Earthquakes and the Richter Scale ...... 417 The Powers of Nanotechnology ....... 418 Prime NumbersBiological Applications of Prime Numbers .... 421 ProbabilityGambling and Probability Myths ....... 425 Probability in Business and Industry ...... 427 Probability, Other Uses .......... 428 Probability in Sports and Entertainment .... 426 Security ............... 424 ProportionArchitecture .............. 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 Quadratic, Cubic, and Quartic EquationsAcceleration .............. 439 Area and Volume ............ 439 Car Tires ............... 439 Guiding Weapons ............ 440 Hospital Size ............. 440 Just in Time Manufacturing ........ 440 RatioAge of Earth .............. 446 Automobile Performance ......... 445 Cleaning Water ............. 446 Cooking ............... 446 Cost of Gas .............. 443 Determination of the Origination of the Moon .. 447 Genetic Traits ............. 443 Healthy Living ............. 446 Length of a Trip ............ 443 Music ................ 445 Optimizing Livestock Production ....... 447 Sports ................ 445 Stem Cell Research ............ 446 Student-Teacher Ratio .......... 445 RoundingAccounting .............. 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 RubricAnalytic Rubrics and Holistic Rubrics ..... 455 General Rubrics and Task-Specific Rubrics .............. 455 Scoring Rubrics ............ 453 SamplingAgriculture .............. 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 ScaleArchitecture .............. 468 Atmospheric Pressure Using Barometer ..... 469 The Calendar ............. 469 Expanse of Scale From the Sub-Atomic to the Universe ........... 471 Interval Scale ............. 466 Linear Scale .............. 465 Logarithmic Scale ............ 465 Map Scale .............. 467 Measuring Wind Strength ......... 469 The Metric System of Measurement ...... 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 Scientific MathAviation and Flights ........... 478 Bridging Chasms ............ 478 Discrete Math ............. 474 Earthquakes and Logarithms ........ 482 Equations and Graphs .......... 476 Estimating Data Used for Assessing Weather ... 477 Functions and Measurements ........ 473 Genetics ............... 483 Logarithms .............. 475 Matrices and Arrays ........... 475 Medical Imaging ............ 480 Rocket Launch ............. 480 Ships ................ 482 Simple Carpentry ............ 479 Trigonometry and the Pythagorean Theorem ... 474 Weather Prediction ........... 476 Wind Chill in Cold Weather ........ 476 Scientific NotationAbsolute 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 Geologic Time Scale and Geology ....... 488 Light Years, the Speed of Light, and Astronomy ........... 486 Medicine ............... 488 Nanotechnology ............ 490 Proteins and Biology ........... 490 Sequences, Sets, and SeriesGenetics ............... 493 Operating On Sets ............ 492 Ordering Things ............ 493 Sequences .............. 491 Series ................ 492 Sets ................. 491 Using Sequences ............ 493 Sports MathBaseball ............... 498 Basketball .............. 499 Cycling—Gear Ratios and How They Work .............. 505 Football—How Far was the Pass Thrown? .... 507 Football Tactics—Math as a Decision-Making Tool ......... 501 Golf Technology ............ 506 Math and the Science of Sport ........ 504 Math and Sports Wagering ......... 508 Math to Understand Sports Performance .... 497 Mathematics and the Judging of Sports ..... 504 Money in Sport—Capology 101....... 507 North American Football ......... 499 Pascal's Triangle and Predicting a Coin Toss ... 500 Predicting the Future: Calling the Coin Toss ... 500 Ratings Percentage Index (RPI) ....... 503 Rules Math .............. 496 Soccer—Free Kicks and the Trajectory of the Ball ............. 506 Understanding the Sports Media Expert .... 502 Square and Cube RootsArchitecture .............. 513 Global Economics ............ 515 Hiopasus's Fatal Discovery ......... 513 Names and Conventions .......... 512 Navigation .............. 514 Pythagorean Theorem .......... 513 Sports ................ 514 Stock Markets ............. 515 StatisticsAnalysis 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 SubtractionSubtraction in Entertainment and Recreation ........... 533 Subtraction in Financial Calculations ..... 531 Subtraction in Politics and Industry ...... 535 Tax Deductions ............. 532 SymmetryArchitecture .............. 541 Exploring Symmetries .......... 539 Fractal Symmetries ........... 541 Imperfect Symmetries .......... 542 Symmetries in Nature .......... 542 TablesConverting Measurements ......... 545 Daily Use ............... 549 Educational Tables ............ 545 Finance ............... 546 Health ................ 548 Math Skills .............. 544 Travel ................ 549 TopologyComputer Networking .......... 555 I.Q. Tests ............... 555 Möbius Strip ............. 555 Visual Analysis ............. 554 Visual Representation ........... 555 TrigonometryChemical 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 Vectors3-D Computer Graphics .......... 572 Drag Racing .............. 572 Land Mine Detection ........... 572 The Magnitude of a Vector ......... 569 Sports Injuries ............. 573 Three-Dimensional Vectors ......... 569 Two-Dimensional Vectors ......... 568 Vector Algebra ............. 570 Vectors in Linear Algebra ......... 571 VolumeBiometric 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 of a Box ............ 575 Volumes of Common Solids ........ 575 Why Thermometers Work ......... 580 Word ProblemsAccounts and VAT ............ 592 Archaeology .............. 585 Architecture .............. 590 Average Height? ............ 593 Banks, Interest Rates, and Introductory Rates ... 591 Bearings and Directions of Travel ....... 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 of a 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 Shortest Links to Establish Electricity 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 Zero-Sum GamesCurrency, Futures, and Stock Markets ..... 597 Experimental Gaming .......... 597 Gambling .............. 596 War ................. 597 |
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