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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.

Mathematics --- Maxima and minima. --- MATHEMATICS / History & Philosophy. --- History. --- Minima --- Math --- Science --- 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.