A popular problem for mathematicians of the 17th century was the brachistochrone curve. Consider two points A and B in a vertical plane, joined by a curve C. In A, a massive particle is dropped with zero initial velocity, and it slides without friction along the curve under the effect of gravity.Wewant to determine the curve C such that the time for the particle to go from A to B is minimum.We note z the altitude and x the abscissa of a point on the curve. The endpoints A and B correspond respectively to (x = a, z = α) and (x = b, z = β).