Translations:The principle of least time/2/en

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Using another analogy, a skier wants to descend on the steepest path available to him at his present position on a hill. The negative gradient is the vector that points in the steepest direction down the hill. This steepest path down is called a fall line. The fall line is always in the direction of the negative gradient of the function whose graph represents the surface of the hill. The fall line and the corresponding flow line coincide. The fall line will change direction as the skier goes downhill from one position to another. A skier feels the fall line and gets visual hints about its location. The skier’s eyes can detect local changes in the steepness of the hill. The skier’s legs indicate whether they are on the fall line or off it. When a skier is skiing the fall line, he feels equal pressure on both legs. All forces are channeled in a direction parallel to the skis. Skiing in any other direction results in pressure on one leg that differs from the pressure on the other. In other words, skiing the fall line means that the skier follows the direction of the negative gradient all the way down the hill.