Today we explore the classic General's Horse Problem. A general needs to return to camp, but his horse becomes thirsty along the way. The horse must first visit the river to drink water before continuing to camp. Our challenge is to find the path that minimizes the total distance traveled.
The solution uses the reflection method. We create a mirror image of the camp by reflecting it across the river. The shortest path from the general to the camp via the river is equivalent to the straight line from the general to the reflected camp. This straight line intersects the river at the optimal drinking point.
The mathematical proof relies on the principle of reflection. When light travels from point A to point B via a mirror, it follows the path where the angle of incidence equals the angle of reflection. This creates the shortest possible path. In our problem, the distance from A to P to B equals the straight-line distance from A to B prime, which is minimal.