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

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Princeton University Press, 22 de jul. 2007 - 372 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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Continguts

and Computers
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All the greatest mathematicians have long
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since recognized that the method presented
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in this book is not only extremely useful
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analysis but that it also contributes greatly
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the solution of physical problems For since
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the fabric of the universe is most perfect
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is the work of a most wise Creator nothing
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be surprised if I tell you I can send you 20 more Cotes then went
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on to reveal that while he was preparing the second edition he
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or Minimum or Solution of Isoperimetric Problems in the Broadest Accepted Sense
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is titled De curvis elasticis You can find a complete annotated English transla tion of the appendix in W A Oldfather et al Leonhard Eulers Elastic C...
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Problem
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Extrema
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whatsoever takes place in the universe
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which some relation of maximum
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minimum does not appear
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the great Swissborn mathematician Leonhard
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Euler in Methodus inveniendi lineas curvas
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maximi minimive proprietate gaudentes sive
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solutio problematis isoperimetrici lattissimo
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sensu accepti 1744
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Newton Cotes who was in charge of preparing the second edition
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of Newtons monumental Principia for publication had a gloomy
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message to deliver stating It is impossible to print the book without
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some faults Events proved him to be correct After the appearance
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of the second edition Newton sent Cotes a list of new corrections
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which prompted Cotes to reply in a letter dated December 22 1713
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of Least Time
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Wine Barrel
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72160
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Problem and a New Minimum
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Brachistochrone
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Solved at last
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Surfaces
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Paving the Shortest Mail Route
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Dynamic Programming
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Appendix C The Sagacity
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Appendix G Beltramis Identity
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Copyright

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Sobre l'autor (2007)

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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