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

This book includes an index.

1. Minimums, Maximums, Derivatives, and Computers 1.1 Introduction 1.2 When Derivatives Don't Work 1.3 Using Algebra to Find Minimums 1.4 A Civil Engineering Problem 1.5 The AM-GM Inequality 1.6 Derivatives from Physics 1.7 Minimizing with a Computer 2. The First Extremal Problems 2.1 The Ancient Confusion of Length and Area 2.2 Dido' Problem and the Isoperimetric Quotient 2.3 Steiner '"Solution" to Dido' Problem 56 2.4 How Steiner Stumbled 2.5 A "Hard "Problem with an Easy Solution 2.6 Fagnano' Problem 3. Medieval Maximization and Some Modern Twists 3.1 The Regiomontanus Problem 3.2 The Saturn Problem 3.3 The Envelope-Folding Problem 3.4 The Pipe-and-Corner Problem 3.5 Regiomontanus Redux 3.6 The Muddy Wheel Problem 4. The Forgotten War of Descartes and Fermat 4.1 Two Very Different Men 4.2 Snell' Law 4.3 Fermat, Tangent Lines, and Extrema 4.4 The Birth of the Derivative 4.5 Derivatives and Tangents 4.6 Snell' Law and the Principle of Least Time 4.7 A Popular Textbook Problem 4.8 Snell' Law and the Rainbow 5. Calculus Steps Forward, Center Stage 5.1 The Derivative:Controversy and Triumph 5.2 Paintings Again, and Kepler' Wine Barrel 5.3 The Mailable Package Paradox 5.4 Projectile Motion in a Gravitational Field 5.5 The Perfect Basketball Shot 5.6 Halley Gunnery Problem 5.7 De L' Hospital and His Pulley Problem, and a New Minimum Principle 5.8 Derivatives and the Rainbow 6. Beyond Calculus 6.1 Galileo'Problem 6.2 The Brachistochrone Problem 6.3 Comparing Galileo and Bernoulli 6.4 The Euler-Lagrange Equation 6.5 The Straight Line and the Brachistochrone 6.6 Galileo' Hanging Chain 6.7 The Catenary Again 6.8 The Isoperimetric Problem, Solved (at last!) 6.9 Minimal Area Surfaces, Plateau' Problem, and Soap Bubbles 6.10 The Human Side of Minimal Area Surfaces 7. The Modern Age Begins 7.1 The Fermat/Steiner Problem 7.2 Digging the Optimal Trench, Paving the Shortest Mail Route, and Least-Cost Paths through Directed Graphs 7.3 The Traveling Salesman Problem 7.4 Minimizing with Inequalities (Linear Programming) 7.5 Minimizing by Working Backwards (Dynamic Programming)