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A Mountain-Climbing Problem

Published online by Cambridge University Press:  20 November 2018

James V. Whittaker
James V. Whittaker*
Affiliation:
University of British Columbia
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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

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Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 873 - 882
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Whyburn, G. T., Analytic topology (New York, 1942).Google Scholar