the line of greatest slope defines the fall line, which is the path a climber will take to gain the most elevation with the shortest possible path.

Map reading

The line of greatest slope has practical significance in map reading. On the terrain it is often far more discernible, even intuitively obvious, rather than accurately picking out the consistent height level on what is likely the undulating uneven ground along the ground represented on the contour line. But knowing that a greatest slope vector is orthogonal to the contour

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