When least is best

How mathematicians discovered many clever ways to make things as small (or as large) as possible

Paul J. Nahin

369 pages, parution le 04/02/2004

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Résumé

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.

L'auteur - Paul J. Nahin

Paul J. Nahin is Professor Emeritus of Electrical Engineering at the University of New Hampshire. He is the author of Duelling Idiots and Other Probability Puzzlers, When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible, and An Imaginary Tale: The Story of I [the square root of -1] (all Princeton).

Sommaire

Minimum, 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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Paul J. Nahin
Parution	04/02/2004
Nb. de pages	369
Format	16 x 24
Couverture	Relié
Poids	698g
Intérieur	Noir et Blanc
EAN13	9780691070780
ISBN13	978-0-691-07078-0