This question seems like it requires calculus, but it actually has a much more clever solution

The video tutorial explores the problem of finding the shortest path that starts at a point P, touches all sides of a polygon, and returns to the starting point. The instructor introduces a simpler problem involving a point Q and uses reflections to demonstrate that the shortest path is a straight line. By reflecting the polygon and its points, the instructor shows how to find the shortest path from P to itself, touching all sides. The method relies on geometric reflections to maintain path length while connecting all sides.

What new insight or understanding did you gain from this video?