## When Least Is Best: |

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, "This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows] obvious delight and enjoyment--he is having fun and it is contagious." " "[ "This book is highly recommended." "A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia." "Nahin delivers maximal mathematical enjoyment with minimal perplexity and boredom. . . . [He lets] general readers in on the thrill of riding high-school geometry and algebra to breakthrough insights. . . . A refreshingly lucid and humanizing approach to mathematics." "Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed."
"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."
- Japanese
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- Chases and Escapes: The Mathematics of Pursuit and Evasion. [Paperback]
- Digital Dice: Computational Solutions to Practical Probability Problems. [Paperback]
- Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills. [Paperback]
- Duelling Idiots and Other Probability Puzzlers. [Paperback]
- An Imaginary Tale: The Story of √-1. [Hardcover and Paperback]
- In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions. [Hardcover]
- The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age. [Hardcover]
- Mrs. Perkins's Electric Quilt: And Other Intriguing Stories of Mathematical Physics. [Hardcover]
- Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction. [Hardcover]
- Will You Be Alive 10 Years from Now? And Numerous Other Curious Questions in Probability. [Hardcover]
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