The Brachistochrone Problem Solved Geometrically: A Very Elementary Approach.

In this article, the author provides a solution to the brachistochrone, shortest time problem using an elementary geometrical approach. He uses geometrical theorems, optics and acoustic techniques to solve the problem. An overview of the physics of the problem, the strategy to solve the problem and step-by-step solution of the problem is given which includes modeling local behavior by the least time model, deriving invariants and generating trajectory.