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When Least Is Best

How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible

Paul Nahin

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Geometrie

Beschreibung

A mathematical journey through the most fascinating problems of extremes and how to solve them

What 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.

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Schlagwörter

Quantity, Derivative, Elementary function, Hyperbolic function, Jensen's inequality, Illustration, Circumference, Curve, Cylinder (geometry), Surface area, Right triangle, Snell's law, Parametric equation, Tangent, Quadratic equation, Real number, Summation, Variable (mathematics), Geometry, Length, Differential calculus, Calculation, Hypotenuse, Square root, Perimeter, Parabola, Addition, Scientific notation, Fermat's principle, Pythagorean theorem, Integer, Mathematician, Mathematical problem, Change of variables, Diameter, Convex function, Refraction, Cartesian coordinate system, Notation, Vertex angle, Clockwise, Equation, Coordinate system, Differential equation, Dimension, Inequality of arithmetic and geometric means, Catenary, Logarithm, Isoperimetric problem, Potential energy, Trigonometric functions, Special case, Ray (optics), Science, Maxima and minima, Iteration, Equilateral triangle, Cycloid, Pierre de Fermat, Chain rule, Instant, Linear programming, Almost surely, Line segment, Arc (geometry), Euler–Lagrange equation, Kinetic energy, Mathematics, Result, Pumping station