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Appendix 3. Landen’s Calculus Solution to the Depressed Cubic Equation
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Chapters in this book
- Frontmatter i
- Contents ix
- Preface xiii
-
PART I. THE PROBLEMS
- Problem 1. A Military Question: Catapult Warfare 3
- Problem 2. A Seemingly Impossible Question: A Shocking Snow Conundrum 4
- Problem 3. Two Math Problems: Algebra and Differential Equations Save the Day 6
- Problem 4. An Escape Problem: Dodge the Truck 8
- Problem 5. The Catapult Again: Where Dead Cows Can’t Go! 9
- Problem 6. Another Math Problem: This One Requires Calculus 10
- Problem 7. If Theory Fails: Monte Carlo Simulation 11
- Problem 8. Monte Carlo and Theory: The Drunkard’s One-Dimensional Random Walk 17
- Problem 9. More Monte Carlo: A Two-Dimensional Random Walk in Paris 19
- Problem 10. Flying with (and against) the Wind: Math for the Modern Traveler 21
- Problem 11. A Combinatorial Problem with Physics Implications: Particles, Energy Levels, and Pauli Exclusion 22
- Problem 12. Mathematical Analysis: By Physical Reasoning 29
- Problem 13. When an Integral Blows Up: Can a Physical Quantity Really Be Infinite? 36
- Problem 14. Is This Easier Than Falling Off a Log? Well, Maybe Not 39
- Problem 15. When the Computer Fails: When Every Day Is a Birthday 47
- Problem 16. When Intuition Fails: Sometimes What Feels Right, Just Isn’t 55
- Problem 17. Computer Simulation of the Physics of NASTYGLASS: Is This Serious? . . . Maybe 60
- Problem 18. The Falling-Raindrop, Variable-Mass Problem: Falling Slower Than Gravity 72
- Problem 19. Beyond the Quadratic: A Cubic Equation and Discontinuous Behavior in a Physical System 81
- Problem 20. Another Cubic Equation: This One Inspired by Jules Verne 93
- Problem 21. Beyond the Cubic: Quartic Equations, Crossed Ladders, Undersea Rocket Launches, and Quintic Equations 103
- Problem 22. Escaping an Atomic Explosion: Why the Enola Gay Survived 114
- Problem 23. “Impossible’’ Math Made Easy: Gauss’s Congruence Arithmetic 122
- Problem 24. Wizard Math: Fourier’s Series, Dirac’s Impulse, and Euler’s Zeta Function 126
- Problem 25. The Euclidean Algorithm: The Zeta Function and Computer Science 137
- Problem 26. One Last Quadratic: Heaviside Locates an Underwater Fish Bite! 147
-
PART II. THE SOLUTIONS
- Einleitung 157
- Appendix 1. MATLAB, Primes, Irrationals, and Continued Fractions 225
- Appendix 2. A Derivation of Brouncker’s Continued Fraction for 4/π 247
- Appendix 3. Landen’s Calculus Solution to the Depressed Cubic Equation 251
- Appendix 4. Solution to Lord Rayleigh’s Rotating-Ring Problem of 1876 261
- Acknowledgments 270
- Index 273
- Also by Paul J. Nahin 281
Chapters in this book
- Frontmatter i
- Contents ix
- Preface xiii
-
PART I. THE PROBLEMS
- Problem 1. A Military Question: Catapult Warfare 3
- Problem 2. A Seemingly Impossible Question: A Shocking Snow Conundrum 4
- Problem 3. Two Math Problems: Algebra and Differential Equations Save the Day 6
- Problem 4. An Escape Problem: Dodge the Truck 8
- Problem 5. The Catapult Again: Where Dead Cows Can’t Go! 9
- Problem 6. Another Math Problem: This One Requires Calculus 10
- Problem 7. If Theory Fails: Monte Carlo Simulation 11
- Problem 8. Monte Carlo and Theory: The Drunkard’s One-Dimensional Random Walk 17
- Problem 9. More Monte Carlo: A Two-Dimensional Random Walk in Paris 19
- Problem 10. Flying with (and against) the Wind: Math for the Modern Traveler 21
- Problem 11. A Combinatorial Problem with Physics Implications: Particles, Energy Levels, and Pauli Exclusion 22
- Problem 12. Mathematical Analysis: By Physical Reasoning 29
- Problem 13. When an Integral Blows Up: Can a Physical Quantity Really Be Infinite? 36
- Problem 14. Is This Easier Than Falling Off a Log? Well, Maybe Not 39
- Problem 15. When the Computer Fails: When Every Day Is a Birthday 47
- Problem 16. When Intuition Fails: Sometimes What Feels Right, Just Isn’t 55
- Problem 17. Computer Simulation of the Physics of NASTYGLASS: Is This Serious? . . . Maybe 60
- Problem 18. The Falling-Raindrop, Variable-Mass Problem: Falling Slower Than Gravity 72
- Problem 19. Beyond the Quadratic: A Cubic Equation and Discontinuous Behavior in a Physical System 81
- Problem 20. Another Cubic Equation: This One Inspired by Jules Verne 93
- Problem 21. Beyond the Cubic: Quartic Equations, Crossed Ladders, Undersea Rocket Launches, and Quintic Equations 103
- Problem 22. Escaping an Atomic Explosion: Why the Enola Gay Survived 114
- Problem 23. “Impossible’’ Math Made Easy: Gauss’s Congruence Arithmetic 122
- Problem 24. Wizard Math: Fourier’s Series, Dirac’s Impulse, and Euler’s Zeta Function 126
- Problem 25. The Euclidean Algorithm: The Zeta Function and Computer Science 137
- Problem 26. One Last Quadratic: Heaviside Locates an Underwater Fish Bite! 147
-
PART II. THE SOLUTIONS
- Einleitung 157
- Appendix 1. MATLAB, Primes, Irrationals, and Continued Fractions 225
- Appendix 2. A Derivation of Brouncker’s Continued Fraction for 4/π 247
- Appendix 3. Landen’s Calculus Solution to the Depressed Cubic Equation 251
- Appendix 4. Solution to Lord Rayleigh’s Rotating-Ring Problem of 1876 261
- Acknowledgments 270
- Index 273
- Also by Paul J. Nahin 281
