# Translations:The principle of least time/1/en

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The gradient is a concept that is familiar to everyone who has climbed a mountain (Figure 8). As a climber goes up the mountain, he experiences the rate of change of elevation. the gradient is the vector (because it has both magnitude and direction) that points in the steepest direction (i.e., the direction in which the rate of change is greatest). The magnitude of the gradient vector is the rate of change of the elevation along this path. Thus, if the climber continually follows the gradient, he will take the steepest path to the top of the mountain. This steepest path is called a flow line.