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Name:When Least Is Best How Mathematicians Discovered~tqw~ darksiderg

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When Least Is Best: How Mathematicians Discovered
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General Information
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Type.................: Ebook
Part Size............: 11,024,837 bytes

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Post Information
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Posted by............: ~tqw~

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Release Notes
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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.

Table of Contents

Preface
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
App. A The AM-GM Inequality 331
App. B The AM-QM Inequality, and Jensen's Inequality 334
App. C "The Sagacity of the Bees" 342
App. D Every Convex Figure Has a Perimeter Bisector 345
App. E The Gravitational Free-Fall Descent Time along a Circle 347
App. F The Area Enclosed by a Closed Curve 352
App. G Beltrami's Identity 359
App. H The Last Word on the Lost Fisherman Problem 361
Acknowledgments 365
Index 367

Product Details

* ISBN: 0691130523
* ISBN-13: 9780691130521
* Format: Paperback, 400pp
* Publisher: Princeton University Press
* Pub. Date: June 2007

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