Imagine paddling in a rowboat from one shore to the opposite shore with no current. The trip takes you 15 minutes. If you return to the river and venture across again, paddling to the opposite shore with the same strokes, but with a stiff current dragging you downstream, will you arrive at the opposite shore in less time, in more time, or in the same time? The time is determined by the motion across the river independent of the speed of the current. The current determines where the boat lands downstream, but does not change the time. In this chapter, we assume that you wish to end up directly across the river and are permitted to walk on the far shore if you land upstream or downstream. What path takes the least time?