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When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible /
What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area? By combining...
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2007.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Minimums, maximums, derivatives, and computers
- The first extremal problems
- Medieval maximization and some modern twists
- The forgotten war of Descartes and Fermat
- Calculus steps forward, center stage
- Beyond calculus
- The modern age begins
- Appendix A. The AM-GM Inequality
- Appendix B. The AM-QM Inequality, and Jensen's Inequality.
- Appendix C. "The sagacity of the bees" (the preface to Book 5 of Pappus' Mathematical collection)
- Appendix D. Every convex figure has a perimeter bisector
- Appendix E. The gravitational free-fall descent time along a circle
- Appendix F. The area enclosed by a closed curve
- Appendix G. Beltrami's identity
- Appendix H. The last word on the lost fisherman problem
- Appendix I. Solution to the new challenge problem.