When least is best: how mathematicians discovered many clever ways to make things as small (or as large) as possible

Description

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.;Minimums, maximums, derivatives, and computers -- The first extremal problems -- Medieval maximization and some modern twists -- The forgotten war of Descartes and Fermat -- Calculus steps forward, center stage -- Beyond calculus -- The modern age begins -- Appendix A. The AM-GM Inequality -- Appendix B. The AM-QM Inequality, and Jensen's Inequality. -- Appendix C. "The sagacity of the bees" (the preface to Book 5 of Pappus' Mathematical collection) -- Appendix D. Every convex figure has a perimeter bisector -- Appendix E. The gravitational free-fall descent time along a circle -- Appendix F. The area enclosed by a closed curve -- Appendix G. Beltrami's identity -- Appendix H. The last word on the lost fisherman problem -- Appendix I. Solution to the new challenge problem.