About Math

PANELS

Panel #, Panel Name, Page in Text

1.1.1: A Wheel of Regular Polygons, 2

1.1.2: Brick Walls, 3

1.2.1: Calculating a Restaurant Payment, 6

1.3.1: Midpoint Repetition, 10

1.3.2: Random Walk 1, 11

1.3.3: Random Walk 2, 11

1.3.4: The Dragon Fractal, 12

1.3.5: Iterating 4x(1–x), 12

1.3.6: Does Sierpinski Work for Squares? 13

1.3.7: One-Dimensional Random Walk, 14

2.1.1: Entering Numbers One Digit at a Time, 17

2.1.2: Evaluating Polynomials by Synthetic Substitution, 19

2.4.1: A Polynomial Equation Solver, 31

3.1.1: Change Seconds to Days, Hours, Minutes and Seconds, 40

3.1.2: Change Fahrenheit Temperature to the Celsius, Kelvin and Rankin Scales, 41

3.1.3: Change Celsius Temperature to the Fahrenheit, Kelvin and Rankin Scales, 41

3.3.1: Percent Change for Linear, Area and Volume Dimensions, 52

3.4.1: Approximation to n! by Stirling's Formula, 57

4.1.1: Change APR (Annual Percent Rate) to APY (Annual Percent Yield), 65

4.1.2: Investment Calculation over a Period of Years or Days, 66

4.2.1: Amortization of a Loan, 70

4.2.2: Converts APR to a Monthly Interest Rate, 70

4.2.3: Determine Present Value of an Ordinary Annuity, 71

4.5.1: Savings Accrued through Monthly or Weekly Deposits, 78

4.5.2: Annuity Due from Investments for Various Time Schedules, 79

4.5.3: Monthly Payments for an Ordinary Annuity, 80

4.6.1: Credit Card Calculations, 82

4.7.1: A Single Evening at the Roulette Table Playing the “Evens”, 86

4.7.2: A Series of Evenings at the Roulette Table Playing the “Evens”, 86

4.7.3: Experiment with the Martingale Strategy, 88

4.7.4: Experiment with the Antimartingale Strategy, 88

5.1.1: Convert Decimal to Binary Numeration, 100

5.2.1: Substitution Cipher: Caesar Shift, 101

5.2.2: Substitution Cipher: “Quick Brown Fox” with Caesar Shift, 102

5.4.1: de Vigenere Cipher, 107

5.4.2: de Vigenere Decipher, 107

5.4.3: The Vicksburg Message, 108

5.5.1: Convert an Integer to x mod N, 110

5.5.2: Reducing p = be mod N, 110

5.5.3: Solving ax = 1 mod y, 111

5.5.4: Modular Shift for PX + Q mod 26, 112

5.5.5: Day of the Week since 1582 CE, 113

5.5.6: Day of the Week prior to 1582 CE, 114

5.6.1: Setting up the RSA Procedure, 116

5.6.2: Coding an RSA Message, 117

5.6.3: Decoding an RSA Message, 117

5.7.1: Prime Factors of Positive Integers, 119

6.3.1: Calculating Approximate Slopes for f(x) = 4x – x2, 136

6.3.2: Polynomial Slope Near a Given x, 142

6.4.1: Calculation of Sum f(x) for Polynomial Functions, 145

6.5.1: Area under y = ¼ x2 – x + 3 between x = 0 and x = 4 for N Rectangles, 148

6.5.2: Approximate Area between Polynomial f(x), the x-axis, x = A and x = B, 151

6.8.1: Derivative of a Polynomial Term, 158

6.8.2: Integrate a Polynomial Term, 158

6.9.1: The nth Fibonacci Number recursively, 164

6.9.2: The nth Fibonacci Number by formula, 164

7.1.1: Random Numbers, 167

7.1.2: Results of Rolling Two Dice, 169

7.1.3: Random Numbers 0 ≤ n < 100,000,000 by Middle Squares, 171

7.2.1: Data for Your Computer's Random Digit Generator, 173

7.2.2: Random Triangles, 173

7.3.1: The Double-Six Problem by Number of Trials, 178

7.4.1: Playing the Dice Game, 179

7.4.2: Playing the MegaMillions Lottery, 181

7.5.1: Playing the St. Petersburg Game, 183

7.5.2: Bernoulli's Formula for a Payment Limit and Game Value, 183

7.5.3: Playing the St. Petersburg Game with Bernoulli's Limits, 184

7.6.1: First Ace, 185

7.6.2: First Ace: Gathering Data, 185

7.6.3: Monte Hall Problem Simulation, 187

7.6.4: Baseball Playoffs, 187

7.6.5: Birthday Problem Trials, 188

7.6.6: Birthday Problem Probabilities, 188

7.6.7: Volleyball Deuce Games, 189

7.6.8: Volleyball Deuce Games: Distribution of Results, 190

7.6.9: Volleyball Deuce Games with Ability Effects, 190

7.6.10: Corner vs. Opposite Seating at Square Tables, 190

7.7.1: Approximating Pi by Random Points, 192

7.7.2: Approximating Pi by Selecting All Points, 193

8.1.1: Counting in our Decimal System, 195

8.1.2: Counting in Other Bases, 2 to 9, 196

8.1.3: Converting from Binary to Decimal, 199

8.1.4: Converting from Decimal to Binary, 199

8.2.1: Addition by Counting On, 199

8.4.1: Multiplying Large Numbers by Hundreds, 210

8.5.1: The Long Division Algorithm, 214

8.5.2: Division Three Digits at a Time (Divisor Less than 1000), 215

8.5.3: Full Division by Hundreds, 215

9.1.1: Integer Powers, 220, 231

9.1.2: Decimal Integers to Binary, 222

9.2.1: Square Root Calculation, 225

9.2.2: Square Root Step-by-Step, 225

9.2.3: Cube Root, 226

9.3.1: Conversion of 0 ≤ x ≤ 1 from Decimal to Binary Representation, 228

9.3.2: Conversion of 0 ≤ x ≤ 1 from Binary to Decimal Representation, 228

9.3.3: Rational Powers BE when 0 ≤ E ≤ 1, 230

9.3.4: Rational Powers BE, 230

9.4.1: Calculation of logbx, 237

9.4.2: Arithmetic, Geometric and Harmonic Means and Root Mean Square, 239

9.5.1: Solving for y in y = Cekx, 240

9.5.2: Solving for x in y = Cekx, 240

9.5.3: Calculates C and k in y = Cekx, given (x1,y1) and (x2,y2), 242

9.6.1: Develops the Logistic Formula given (0,y1), (x2,y2) and L, 249

9.6.2: Solves for y given x and Logistic Values (x1,y1), (x2,y2) and L, 250

9.6.3: Solves for x given y and Logistic Values (x1,y1), (x2,y2) and L, 250

9.6.4: Calculates the number of mice in successive breeding cycles, 252

10.1.1: Triangle Area by S = ½ bh, 254

10.1.2: SAS Triangle Area, 254

10.1.3: SSS Triangle Area, 254

10.1.4: ASA Triangle Area, 255

10.1.5: ASS Triangle Area, 255

10.4.1: Area of a Spherical Triangle, 267

10.4.2: Convert Angles from DMS to DEC, 267

10.4.3: Convert Angles from DEC to DMS, 268

10.4.4: Distance to the Horizon, 269

10.5.1: Longitude to Universal Time Zone, 274

10.5.2: Local Sun Zenith and Universal Time Zone to Longitude, 274

10.5.3: Longitude and Universal Time Zone to Local Sun Zenith, 275

10.6.1: Distance and Direction between Two Locations, 276