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

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

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.

 

Què opinen els usuaris - Escriviu una ressenya

No hem trobat cap ressenya als llocs habituals.

Pàgines seleccionades

Continguts

1 Minimums Maximums Derivatives and Computers
1
2 The First Extremal Problems
37
3 Medieval Maximization and Some Modern Twists
71
4 The Forgotten War of Descartes and Fermat
99
5 Calculus Steps Forward Center Stage
140
6 Beyond Calculus
200
7 The Modern Age Begins
279
Appendix A The AMGM Inequality
331
Appendix D Every Convex Figure Has a Perimeter Bisector
345
Appendix E The Gravitational FreeFall Descent Time along a Circle
347
Appendix F The Area Enclosed by a Closed Curve
352
Appendix G Beltramis Identity
359
Appendix H The Last Word on the Lost Fisherman Problem
361
Appendix I Solution to the New Challenge Problem
364
Acknowledgments
367
Index
369

Appendix B The AMQM Inequality and Jensens Inequality
334
Appendix C The Sagacity of the Bees the preface to Book 5 of Pappus Mathematical Collection
342

Altres edicions - Mostra-ho tot

Frases i termes més freqüents

Quant a 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).

Informació bibliogràfica