Learning solutions provided for the Brachistochrone Problem

The Brachistochrone problem, meaning in greek "shortest time", is the question regarding what is the shape of the path to slide a point mass between two arbitrary points with a height difference in the shortest time possible, while considering only the action of a constant gravitational force applied on it. This project will present the problem, and the solutions provided for the problem by Johann Brenoulli, and through calculus of variations