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On catching a moving particle by narrow strips. (English) Zbl 0586.51017

For a particle moving in a Euclidean plane the following theorem is proved and commented: For any real positive numbers d and k there exists a d-strip such that the time the particle spend there is at least k. (A d-strip is the set of points at a distance not greater than d/2 from a straight line.)
Reviewer: Dan Brânzei

MSC:

51M05 Euclidean geometries (general) and generalizations
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References:

[1] Gerver, Joseph, L. and Thomas Ramsey, L., ’On Certain Sequences of Lattice Points’, Pacific J. Math. 83 (2) (1979), 357–363. · Zbl 0387.60074
[2] Montgomery, P. L., ’Solution of Problem 5811 (proposed by T. C. Brown)’, Amer. Math. Monthly 79 (1972), 1143–1144.
[3] Pomerance, Carl, ’Collinear Subsets of Lattice Point Sequences – An Analog of Szemeredi’s Theorem’, J. Comb. Theory A28 (1980), 140–149. · Zbl 0428.10027
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