How to climb the face of a mountain


The shortest line connecting a point at the base of a mountain with the top is a geodesic on the surface of the mountain. But this path is often unpracticable since the inclination of the geodesic with respect the horizontal is often too high to being directly overcome by a climber. We here propose a strategy for reaching the top along curves not exceeding the maximum inclination superable by the climber.We here discuss two particular examples for which an explicit solution is obtainable in terms of elliptic functions.

DOI Code: 10.1285/i15900932v27n2p249

Optimal paths

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