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020			_a9780691130521
040			_aIIITD
082			_a511.66 _bNAH-W
100			_aNahin, Paul J.
245			_aWhen least is best : _bhow mathematicians discovered many clever ways to make things as small (or as large) as possible _cby Paul J. Nahin
260			_bPrinceton University Press, _aNew Jersey : _c©2004
300			_axxvi, 372 p. : _bill. ; _c24 cm.
504			_aThis book includes an index.
505			_t1. Minimums, Maximums, Derivatives, and Computers _t1.1 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 _t2. The First Extremal Problems _t2.1 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 _t3. Medieval Maximization and Some Modern Twists _t3.1 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 _t4. The Forgotten War of Descartes and Fermat _t4.1 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 _t5. Calculus Steps Forward, Center Stage _t5.1 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 _t6. Beyond Calculus _t6.1 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 _t7. The Modern Age Begins _t7.1 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)
650			_aMathematics
650			_aMaxima and minima
650			_aMathematical optimization
650			_aCalculus
942			_2ddc _cBK
999			_c172019 _d172019