Heron's mirror problem
You stand at point A, and a friend stands at point B, both on the same side of a long straight mirror. You want to glance at the mirror and catch your friend's reflection with the shortest possible path from your eye to the mirror to your friend. Which point on the mirror do you aim for?
Reveal the answer
Reflect B across the mirror line to get a point B'. The straight line from A to B' crosses the mirror at exactly the point that minimizes the total path length, and that point is precisely where the angle of incidence equals the angle of reflection. Heron of Alexandria proved this around the 1st century AD in his Catoptrica, making it one of the earliest known 'least path' principles in physics, centuries before anyone knew light was doing the same calculation every time it bounces.