The mountain climbers' problem
Proc. Amer. Math. Soc. 117 (1993), 89-97
Primary 26A12; Secondary 26A15, 26A48
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Abstract: We show that two climbers can climb a mountain in such a way that at each moment they are at the same height above the sea level, supposing that the mountain has no plateau. That is, if and are continuous functions mapping to with and , and if neither nor has an interval of constancy then there exist continuous functions and satisfying , and .
E. Goodman, János
Pach, and Chee-K.
Yap, Mountain climbing, ladder moving, and the ring-width of a
polygon, Amer. Math. Monthly 96 (1989), no. 6,
999412 (90h:52010), http://dx.doi.org/10.2307/2323971
V. Whittaker, A mountain-climbing problem, Canad. J. Math.
18 (1966), 873–882. MR 0196013
- J. E. Goodman, J. Pach, and C. K. Yap, Mountain climbing, ladder moving, and the ring width of a polygon, Amer. Math. Monthly 96 (1989), 494-510. MR 999412 (90h:52010)
- James V. Whittaker, A mountain-climbing problem, Canad. J. Math 18 (1966), 873-882. MR 0196013 (33:4208)
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