Donald Benson provided an elementary solution to it in a horizontal frame using Cauchy's inequality, and the absence of an explicit x term results in a simplified version that can be solved by the Beltrami identity.
Donald Benson provided an elementary solution to it in a horizontal frame using Cauchy's inequality, and the absence of an explicit x term results in a simplified version that can be solved by the Beltrami identity. An approach analogous to optics invokes Fermat's Principle and Snell's Law, which was employed by Johann Bernoulli, while Leibniz, Newton, and L'Hopital solved it using the calculus of variations. For 10 points, identify this problem which seeks the path connecting two points on which an object can slide under the influence of gravity in "least time."
Donald Benson provided an elementary solution to it in a horizontal frame using Cauchy's inequality, and the absence of an explicit x term results in a simplified version that can be solved by the Beltrami identity.
{Brachistochrone} problem