Brachistochrone Problem

The Brachistochrone Problem is a classic challenge in physics and calculus that seeks the fastest path for an object to slide under gravity from one point to another, not necessarily in a straight line. It shows that the quickest route is a specific curve called the cycloid, rather than a direct or simple path. This problem helps us understand how optimal shapes and paths are determined by balancing distance and gravity, illustrating principles behind designing efficient routes and systems in physics and engineering.