Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 737.52006
Autor: Erdös, Paul; Fishburn, Peter; Füredi, Zoltan
Title: Midpoints of diagonals of convex n-gons. (In English)
Source: SIAM J. Discrete Math. 4, No.3, 329-341 (1991).
Review: The authors' abstract: ``Let f(n) be the minimum over all convex planar n-gons of the number of different midpoints of the {n \choose 2} line segments, or diagonals, between distinct vertices. It is proved that f(n) is between approximately 0.8\binom{n}{2} and 0.9\binom{n}{2}. The upper bound uses the fact that the number of multiple midpoints, shared by two or more diagonals, can be as great as about \binom{n}{2}/10. Cases for which the number of midpoints is at least \lceil n(n- 2)/2\rceil+1, the number for a regular n-gon when n is even, are noted.''.
Reviewer: J.C.Dupin (Valenciennes)
Classif.: * 52A37 Other problems of combinatorial convexity
52A10 Convex sets in 2 dimensions (including convex curves)
Keywords: convex n-gons; diagonal midpoints; multiple midpoints
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