Geodesic
A Mountain-Climbing Problem
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 873-882

Voir la notice de l'article provenant de la source Cambridge University Press

Suppose that two men stand at the same elevation on opposite sides of a mountain range and begin to climb in such a way that their elevations remain equal at all times. Will they ever meet along the way? It is this question, restated in mathematical terms, that we shall consider. We replace the mountain range by the graph of a continuous, real-valued function f(x) defined for x ∈ [0, 1], where f(0) = f(1) = 0, and we ask whether there exist continuous mappings φ(t), ψ(t) from [0, 1] into [0, 1] such that 1 2 
Whittaker, James V. A Mountain-Climbing Problem. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 873-882. doi: 10.4153/CJM-1966-087-x
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[1] 1. Whyburn, G. T., Analytic topology (New York, 1942). Google Scholar

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