Page vii - Contents

11.     Circular Functions versus Hyperbolic Functions - Page 243

1.    The Circle and the Hyperbola - Page 245

2.    Circular Angles – Circular Radians - Page 246

3.    Hyperbolic Angles – Hyperbolic Radians - Page 251

12. Hyperbola and some of its Properties - Page 259

1. The Hyperbola in the x-y Coordinates - Page 261

2. Rotation of a coordinate system - Page 262

3. The Hyperbola in the u-v Coordinates - Page 263

4. Squaring a Hyperbola – Part 1 - Page 264

5. Squaring a Hyperbola – Part 2 - Page 266

6. Hyperbola and the Arithmetic/Geometric Progressions - Page 268

7. Squaring a Hyperbola – Part 3 - Page 270

13. The Gudermannian Angles - Page 273

1. The Gudermannian Angles - Page 275

2. Geometrical Interpretation of the Gudermannian - Page 280

14. Prime Number Theorem - Page 285

1. Some Trigonometry - Page 287

2. The Prime Number Theorem – A Proof - Page 291

15. Riemann Hypothesis – Equivalent For - Page 299

1. Riemann Hypothesis – A Proof - Page 301

16. Trigonometric Generalizations - Page 327

1. A Generalization of De Moivre’s Theorem - Page 329

2. Multiple Angles Relationships - Page 333

17. Harmonic Actions - Page 335

1. Circular Action - Page 337

2. Hyperbolic Action - Page 339

3. Exponential Action - Page 341