When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible

Princeton University Press, 23 d’oct. 2011 - 392 pàgines

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 the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot.

Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics.


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Pàgines seleccionades


1 Minimums Maximums Derivatives and Computers
2 The First Extremal Problems
3 Medieval Maximization and Some Modern Twists
4 The Forgotten War of Descartes and Fermat
5 Calculus Steps Forward Center Stage
6 Beyond Calculus
7 The Modern Age Begins
Appendix A The AMGM Inequality
Appendix D Every Convex Figure Has a Perimeter Bisector
Appendix E The Gravitational FreeFall Descent Time along a Circle
Appendix F The Area Enclosed by a Closed Curve
Appendix G Beltramis Identity
Appendix H The Last Word on the Lost Fisherman Problem
Appendix I Solution to the New Challenge Problem

Appendix B The AMQM Inequality and Jensens Inequality
Appendix C The Sagacity of the Bees the preface to Book 5 of Pappus Mathematical Collection

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Sobre l'autor (2011)

Paul J. Nahin is Professor Emeritus of Electrical Engineering at the University of New Hampshire. He is the author of many books, including the bestselling An Imaginary Tale: The Story of the Square Root of Minus One, Duelling Idiots and Other Probability Puzzlers, and Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (all Princeton).

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