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**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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