When Least Is Best : : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / / Paul J. Nahin.
A mathematical journey through the most fascinating problems of extremes and how to solve themWhat 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...
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Nahin, Paul J., author. aut http://id.loc.gov/vocabulary/relators/aut When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / Paul J. Nahin. Princeton, NJ : Princeton University Press, [2021] ©2003 1 online resource (392 p.) : 99 b/w illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Science Library ; 114 Frontmatter -- Contents -- Preface to the 2021 Edition -- Preface to the 2007 Paperback Edition -- Preface -- 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’s Problem and the Isoperimetric Quotient -- 2.3 Steiner’s “Solution” to Dido’s Problem -- 2.4 How Steiner Stumbled -- 2.5 A “Hard” Problem with an Easy Solution -- 2.6 Fagnano’s 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’s Law -- 4.3 Fermat, Tangent Lines, and Extrema -- 4.4 The Birth of the Derivative -- 4.5 Derivatives and Tangents -- 4.6 Snell’s Law and the Principle of Least Time -- 4.7 A Popular Textbook Problem -- 4.8 Snell’s Law and the Rainbow -- 5. Calculus Steps Forward, Center Stage -- 5.1 The Derivative: Controversy and Triumph -- 5.2 Paintings Again, and Kepler’s 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’s 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’s 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’s Hanging Chain -- 6.7 The Catenary Again -- 6.8 The Isoperimetric Problem, Solved (at last!) -- 6.9 Minimal Area Surfaces, Plateau’s 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) -- 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 -- Acknowledgments -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star A mathematical journey through the most fascinating problems of extremes and how to solve themWhat 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. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Jun 2022) Mathematics History. Maxima and minima. MATHEMATICS / History & Philosophy. bisacsh AP Calculus. Addition. Almost surely. American Mathematical Monthly. Arc (geometry). Calculation. Cambridge University Press. Cartesian coordinate system. Catenary. Central angle. Chain rule. Change of variables. Circumference. Clockwise. Convex function. Coordinate system. Curve. Cycloid. Cylinder (geometry). Derivative. Diameter. Differential calculus. Differential equation. Dimension. Dynamic programming. Elementary function. Equation. Equilateral triangle. Euler–Lagrange equation. Fermat's principle. Fluxion. Geometry. Honeycomb conjecture. Hyperbolic function. Hypotenuse. Illustration. Inequality of arithmetic and geometric means. Instant. Integer. Isoperimetric problem. Iteration. Jensen's inequality. Johann Bernoulli. Kinetic energy. Length. Line (geometry). Line segment. Linear programming. Logarithm. Mathematical maturity. Mathematical problem. Mathematician. Mathematics. Newton's method. Notation. Parabola. Parametric equation. Partial derivative. Perimeter. Philosopher. Physicist. Pierre de Fermat. Polygon. Polynomial. Potential energy. Princeton University Press. Projectile. Pumping station. Pythagorean theorem. Quadratic equation. Quadratic formula. Quantity. Ray (optics). Real number. Rectangle. Refraction. Refractive index. Regiomontanus. Requirement. Result. Right angle. Right triangle. Science. Scientific notation. Second derivative. Semicircle. Sign (mathematics). Simple algebra. Simplex algorithm. Snell's law. Special case. Square root. Summation. Surface area. Tangent. Trigonometric functions. Variable (mathematics). Vertex angle. Writing. Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 English 9783110754001 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2021 9783110753776 ZDB-23-DGG Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 https://doi.org/10.1515/9780691220383?locatt=mode:legacy https://www.degruyter.com/isbn/9780691220383 Cover https://www.degruyter.com/document/cover/isbn/9780691220383/original |
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English |
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Nahin, Paul J., Nahin, Paul J., |
spellingShingle |
Nahin, Paul J., Nahin, Paul J., When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / Princeton Science Library ; Frontmatter -- Contents -- Preface to the 2021 Edition -- Preface to the 2007 Paperback Edition -- Preface -- 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’s Problem and the Isoperimetric Quotient -- 2.3 Steiner’s “Solution” to Dido’s Problem -- 2.4 How Steiner Stumbled -- 2.5 A “Hard” Problem with an Easy Solution -- 2.6 Fagnano’s 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’s Law -- 4.3 Fermat, Tangent Lines, and Extrema -- 4.4 The Birth of the Derivative -- 4.5 Derivatives and Tangents -- 4.6 Snell’s Law and the Principle of Least Time -- 4.7 A Popular Textbook Problem -- 4.8 Snell’s Law and the Rainbow -- 5. Calculus Steps Forward, Center Stage -- 5.1 The Derivative: Controversy and Triumph -- 5.2 Paintings Again, and Kepler’s 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’s 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’s 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’s Hanging Chain -- 6.7 The Catenary Again -- 6.8 The Isoperimetric Problem, Solved (at last!) -- 6.9 Minimal Area Surfaces, Plateau’s 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) -- 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 -- Acknowledgments -- Index |
author_facet |
Nahin, Paul J., Nahin, Paul J., |
author_variant |
p j n pj pjn p j n pj pjn |
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VerfasserIn VerfasserIn |
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Nahin, Paul J., |
title |
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / |
title_sub |
How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / |
title_full |
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / Paul J. Nahin. |
title_fullStr |
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / Paul J. Nahin. |
title_full_unstemmed |
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / Paul J. Nahin. |
title_auth |
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / |
title_alt |
Frontmatter -- Contents -- Preface to the 2021 Edition -- Preface to the 2007 Paperback Edition -- Preface -- 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’s Problem and the Isoperimetric Quotient -- 2.3 Steiner’s “Solution” to Dido’s Problem -- 2.4 How Steiner Stumbled -- 2.5 A “Hard” Problem with an Easy Solution -- 2.6 Fagnano’s 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’s Law -- 4.3 Fermat, Tangent Lines, and Extrema -- 4.4 The Birth of the Derivative -- 4.5 Derivatives and Tangents -- 4.6 Snell’s Law and the Principle of Least Time -- 4.7 A Popular Textbook Problem -- 4.8 Snell’s Law and the Rainbow -- 5. Calculus Steps Forward, Center Stage -- 5.1 The Derivative: Controversy and Triumph -- 5.2 Paintings Again, and Kepler’s 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’s 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’s 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’s Hanging Chain -- 6.7 The Catenary Again -- 6.8 The Isoperimetric Problem, Solved (at last!) -- 6.9 Minimal Area Surfaces, Plateau’s 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) -- 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 -- Acknowledgments -- Index |
title_new |
When Least Is Best : |
title_sort |
when least is best : how mathematicians discovered many clever ways to make things as small (or as large) as possible / |
series |
Princeton Science Library ; |
series2 |
Princeton Science Library ; |
publisher |
Princeton University Press, |
publishDate |
2021 |
physical |
1 online resource (392 p.) : 99 b/w illus. |
contents |
Frontmatter -- Contents -- Preface to the 2021 Edition -- Preface to the 2007 Paperback Edition -- Preface -- 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’s Problem and the Isoperimetric Quotient -- 2.3 Steiner’s “Solution” to Dido’s Problem -- 2.4 How Steiner Stumbled -- 2.5 A “Hard” Problem with an Easy Solution -- 2.6 Fagnano’s 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’s Law -- 4.3 Fermat, Tangent Lines, and Extrema -- 4.4 The Birth of the Derivative -- 4.5 Derivatives and Tangents -- 4.6 Snell’s Law and the Principle of Least Time -- 4.7 A Popular Textbook Problem -- 4.8 Snell’s Law and the Rainbow -- 5. Calculus Steps Forward, Center Stage -- 5.1 The Derivative: Controversy and Triumph -- 5.2 Paintings Again, and Kepler’s 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’s 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’s 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’s Hanging Chain -- 6.7 The Catenary Again -- 6.8 The Isoperimetric Problem, Solved (at last!) -- 6.9 Minimal Area Surfaces, Plateau’s 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) -- 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 -- Acknowledgments -- Index |
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When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible / |
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The Forgotten War of Descartes and Fermat -- </subfield><subfield code="t">4.1 Two Very Different Men -- </subfield><subfield code="t">4.2 Snell’s Law -- </subfield><subfield code="t">4.3 Fermat, Tangent Lines, and Extrema -- </subfield><subfield code="t">4.4 The Birth of the Derivative -- </subfield><subfield code="t">4.5 Derivatives and Tangents -- </subfield><subfield code="t">4.6 Snell’s Law and the Principle of Least Time -- </subfield><subfield code="t">4.7 A Popular Textbook Problem -- </subfield><subfield code="t">4.8 Snell’s Law and the Rainbow -- </subfield><subfield code="t">5. Calculus Steps Forward, Center Stage -- </subfield><subfield code="t">5.1 The Derivative: Controversy and Triumph -- </subfield><subfield code="t">5.2 Paintings Again, and Kepler’s Wine Barrel -- </subfield><subfield code="t">5.3 The Mailable Package Paradox -- </subfield><subfield code="t">5.4 Projectile Motion in a Gravitational Field -- </subfield><subfield code="t">5.5 The Perfect Basketball Shot -- </subfield><subfield code="t">5.6 Halley’s Gunnery Problem -- </subfield><subfield code="t">5.7 De L’Hospital and His Pulley Problem, and a New Minimum Principle -- </subfield><subfield code="t">5.8 Derivatives and the Rainbow -- </subfield><subfield code="t">6. Beyond Calculus -- </subfield><subfield code="t">6.1 Galileo’s Problem -- </subfield><subfield code="t">6.2 The Brachistochrone Problem -- </subfield><subfield code="t">6.3 Comparing Galileo and Bernoulli -- </subfield><subfield code="t">6.4 The Euler-Lagrange Equation -- </subfield><subfield code="t">6.5 The Straight Line and the Brachistochrone -- </subfield><subfield code="t">6.6 Galileo’s Hanging Chain -- </subfield><subfield code="t">6.7 The Catenary Again -- </subfield><subfield code="t">6.8 The Isoperimetric Problem, Solved (at last!) -- </subfield><subfield code="t">6.9 Minimal Area Surfaces, Plateau’s Problem, and Soap Bubbles -- </subfield><subfield code="t">6.10 The Human Side of Minimal Area Surfaces -- </subfield><subfield code="t">7. The Modern Age Begins -- </subfield><subfield code="t">7.1 The Fermat/Steiner Problem -- </subfield><subfield code="t">7.2 Digging the Optimal Trench, Paving the Shortest Mail Route, and Least-Cost Paths through Directed Graphs -- </subfield><subfield code="t">7.3 The Traveling Salesman Problem -- </subfield><subfield code="t">7.4 Minimizing with Inequalities (Linear Programming) -- </subfield><subfield code="t">7.5 Minimizing by Working Backwards (Dynamic Programming) -- </subfield><subfield code="t">Appendix A. The AM-GM Inequality -- </subfield><subfield code="t">Appendix B. The AM-QM Inequality, and Jensen’s Inequality -- </subfield><subfield code="t">Appendix C. “The Sagacity of the Bees” (the preface to Book 5 of Pappus’ Mathematical Collection) -- </subfield><subfield code="t">Appendix D. Every Convex Figure Has a Perimeter Bisector -- </subfield><subfield code="t">Appendix E. The Gravitational Free-Fall Descent Time along a Circle -- </subfield><subfield code="t">Appendix F. The Area Enclosed by a Closed Curve -- </subfield><subfield code="t">Appendix G. Beltrami’s Identity -- </subfield><subfield code="t">Appendix H. The Last Word on the Lost Fisherman Problem -- </subfield><subfield code="t">Appendix I. Solution to the New Challenge Problem -- </subfield><subfield code="t">Acknowledgments -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">A mathematical journey through the most fascinating problems of extremes and how to solve themWhat 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.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Jun 2022)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield><subfield code="x">History.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Maxima and minima.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / History & Philosophy.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">AP Calculus.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Addition.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Almost surely.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">American Mathematical Monthly.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Arc (geometry).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Calculation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cambridge University Press.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cartesian coordinate system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Catenary.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Central angle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Chain rule.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Change of variables.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Circumference.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Clockwise.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Convex function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Coordinate system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Curve.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cycloid.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Cylinder (geometry).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Derivative.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Diameter.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Differential calculus.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Differential equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Dimension.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Dynamic programming.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Elementary function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Equilateral triangle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Euler–Lagrange equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fermat's principle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fluxion.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Honeycomb conjecture.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Hyperbolic function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Hypotenuse.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Illustration.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Inequality of arithmetic and geometric means.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Instant.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Integer.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Isoperimetric problem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Iteration.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Jensen's inequality.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Johann Bernoulli.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Kinetic energy.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Length.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Line (geometry).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Line segment.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Linear programming.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Logarithm.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematical maturity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematical problem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematician.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Maxima and minima.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Newton's method.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parabola.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parametric equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Partial derivative.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Perimeter.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Philosopher.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Physicist.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Pierre de Fermat.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polygon.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polynomial.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Potential energy.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Princeton University Press.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Projectile.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Pumping station.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Pythagorean theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quadratic equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quadratic formula.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quantity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Ray (optics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Real number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Rectangle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Refraction.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Refractive index.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Regiomontanus.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Requirement.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Result.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Right angle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Right triangle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Science.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Scientific notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Second derivative.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Semicircle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sign (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simple algebra.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simplex algorithm.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Snell's law.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Square root.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Surface area.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tangent.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trigonometric functions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variable (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vertex angle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Writing.</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2021 English</subfield><subfield code="z">9783110754001</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">EBOOK PACKAGE COMPLETE 2021</subfield><subfield code="z">9783110753776</subfield><subfield code="o">ZDB-23-DGG</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Backlist 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