Appendix F. The Area Enclosed by a Closed Curve

Chapters in this book

1. Frontmatter i
2. Contents ix
3. Preface to the Paperback Edition xiii
4. Preface xxi
5. 1. Minimums, Maximums, Derivatives, and Computers 1
6. 2. The First Extremal Problems 37
7. 3. Medieval Maximization and Some Modern Twists 71
8. 4. The Forgotten War of Descartes and Fermat 99
9. 5. Calculus Steps Forward, Center Stage 140
10. 6. Beyond Calculus 200
11. 7. The Modern Age Begins 279
12. Appendix A. The AM-GM Inequality 331
13. Appendix B. The AM-QM Inequality, and Jensen’s Inequality 334
14. Appendix C. “The Sagacity of the Bees” 342
15. Appendix D. Every Convex Figure Has a Perimeter Bisector 345
16. Appendix E. The Gravitational Free-Fall Descent Time along a Circle 347
17. Appendix F. The Area Enclosed by a Closed Curve 352
18. Appendix G. Beltrami’s Identity 359
19. Appendix H. The Last Word on the Lost Fisherman Problem 361
20. Appendix I. Solution to the New Challenge Problem 364
21. Acknowledgments 367
22. Index 369