In this Book
- When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible
- Book
- 2021
- Published by: Princeton University Press
- Series: Princeton Science Library
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.
Table of Contents
- Title, Copyright, Dedication
- pp. ii-viii
- Preface to the 2021 Edition
- pp. xiii-xviii
- Preface to the 2007 Paperback Edition
- pp. xix-xxvi
- 2. The First Extremal Problems
- pp. 37-70
- 5. Calculus Steps Forward, Center Stage
- pp. 140-199
- 6. Beyond Calculus
- pp. 200-278
- 7. The Modern Age Begins
- pp. 279-330
- Appendix A. The AM-GM Inequality
- pp. 331-333
- Appendix C. "The Sagacity of the Bees"
- pp. 342-344
- Appendix G. Beltrami's Identity
- pp. 359-360
- Acknowledgments
- pp. 367-368