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When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible
A mathematical journey through the most fascinating problems of extremes and how to solve them
What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes-with values becoming as small (or as large) as possible-and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.
What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes-with values becoming as small (or as large) as possible-and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.
406 pages, Paperback
First published January 1, 2003
17 people are currently reading
318 people want to read
About the author
Paul J. Nahin
53 books124 followersPaul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire and the author of many best-selling popular math books, including The Logician and the Engineer and Will You Be Alive 10 Years from Now? (both Princeton).
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Displaying 1 - 6 of 6 reviews
August 2, 2020
Everyone learns in calculus that the way to find the minimum or maximum of a function is to take the derivative of the function, set it to zero, then solve for x. Easy peasy, right? OK, but then how did mathematicians solve that type of problem *before* calculus was invented??
Any question of the sort "How small or large can something be, under these conditions/constraints?" is an optimization question. This book is Paul Nahin's history of the subject:
1) How you're supposed to solve these problems today.
2) How the Greeks/Egyptions/Phoenicians solved these types of problems.
3) How medieval Europeans solved these types of problems.
4) Why René Descartes was such a dick to Pierre de Fermat.
5) Artillery and rainbows.
6) Calculus is great, yes, but now what?
7) How are these problems solved today when there's more than one variable?
This was a random find at a bookshop in Austin and I'm glad I found it. I read it a little bit at a time on the bus to work each morning. Very easy to digest, and fun to think about. Strongly recommended for anyone who made it through those first couple of semesters of calculus.
Marilyn vos Savant makes an appearance on p196, because of course she does. The author is obsessed with her and will not let go. That seems to be the only downside to Nahin's books.
If you're not sure whether this book is right for you, the preface (which you can view in Google Books) asks whether you can take a limit and whether you understand how to do integrals. If you can handle both, then go for it!
Any question of the sort "How small or large can something be, under these conditions/constraints?" is an optimization question. This book is Paul Nahin's history of the subject:
1) How you're supposed to solve these problems today.
2) How the Greeks/Egyptions/Phoenicians solved these types of problems.
3) How medieval Europeans solved these types of problems.
4) Why René Descartes was such a dick to Pierre de Fermat.
5) Artillery and rainbows.
6) Calculus is great, yes, but now what?
7) How are these problems solved today when there's more than one variable?
This was a random find at a bookshop in Austin and I'm glad I found it. I read it a little bit at a time on the bus to work each morning. Very easy to digest, and fun to think about. Strongly recommended for anyone who made it through those first couple of semesters of calculus.
Marilyn vos Savant makes an appearance on p196, because of course she does. The author is obsessed with her and will not let go. That seems to be the only downside to Nahin's books.
If you're not sure whether this book is right for you, the preface (which you can view in Google Books) asks whether you can take a limit and whether you understand how to do integrals. If you can handle both, then go for it!
February 21, 2019
Tediously spells it every derivation but the treatment of history of mathematics and famous optimization problems such as ballistics and basketball and double/triple/etc rainbows is great.
August 7, 2018
Great book on optimization.
June 3, 2016
For the mathematically inclined, this book takes you through many problems/calculations in determining various extrema problems and learning various well-known real life examples. Included is some discussion of the history of these problems.
March 3, 2016
A must re-read. Finally Euler Lagrange equation made sense through it.
Displaying 1 - 6 of 6 reviews