The Brachistochrone problem... A classic example of the calculus of variations is to find the brachistochrone, defined as that smooth curve joining two points A and B (not underneath one another) along which a particle will slide from A to B under gravity in the fastest possible time. The path of the quickest descent is not a straight line but a brachistochrone curve. Johann Bernoulli investigated the Brachistochrone problem and offered a challenge, specifically aimed at his older Brother Jacob