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

Nahin, Paul J.

Hardcover

ISBN 10: 0691070784 ISBN 13: 9780691070780

Publisher: Princeton University Press, 2003

Synopsis

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.

About this title

About the Author

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).

From the Back Cover

"This is a delightful account of how the concepts of maxima, minima, and differentiation evolved with time. The level of mathematical sophistication is neither abstract nor superficial and it should appeal to a wide audience."--Ali H. Sayed, University of California, Los Angeles

"When Least Is Best is an illustrative historical walk through optimization problems as solved by mathematicians and scientists. Although many of us associate solving optimization with calculus, Paul J. Nahin shows here that many key problems were posed and solved long before calculus was developed."--Mary Ann B. Freeman, Math Team Development Manager, Mathworks

From the Inside Flap

"This is a delightful account of how the concepts of maxima, minima, and differentiation evolved with time. The level of mathematical sophistication is neither abstract nor superficial and it should appeal to a wide audience."--Ali H. Sayed, University of California, Los Angeles

"When Least Is Best is an illustrative historical walk through optimization problems as solved by mathematicians and scientists. Although many of us associate solving optimization with calculus, Paul J. Nahin shows here that many key problems were posed and solved long before calculus was developed."--Mary Ann B. Freeman, Math Team Development Manager, Mathworks

Reviews

How can a factory manager minimize breakdowns? How can a disoriented hiker reach her car in the least possible time? In answering questions such as these, engineer Nahin delivers maximal mathematical enjoyment with minimal perplexity and boredom. Classical minimization problems allow Nahin to showcase the ingenuity of ancient mathematicians--and to let general readers in on the thrill of riding high-school geometry and algebra to breakthrough insights. Knowledgeable readers will probably anticipate the eventual transition from subtle geometry to complex calculus. But even specialists may learn from Nahin's chronicle of how the often-forgotten tangents of Pierre de Fermat paved the way to the calculus of Newton and Leibniz. In addition, Nahin deftly interweaves episodes from the lives of its discoverers: a rash Belgian theorist loses his sight staring at the sun; a jealous Swiss mathematician denies his own son credit for groundbreaking work. A refreshingly lucid and humanizing approach to mathematics. Bryce Christensen
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Edition details

• Publisher: Princeton University Press
• Publication date: 2003
• Language: English
• ISBN 10: 0691070784
• ISBN 13: 9780691070780
• Binding: Hardcover
• Number of pages: 370