##
**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 844.52002

**Autor: ** Erdös, Paul; Soifer, Alexander

**Title: ** Triangles in convex polygons. (In English)

**Source: ** Geombinatorics 2, No.4, 72-74 (1993).

**Review: ** The authors pose the following ``maximin'' problem.

Determine \Delta (n,k): = **max** (**max** \Delta (V)). Here V is a finite set of n+k points in the Euclidean plane such that the convex hull conv V of V has area 1 and n points of V are vertices of conv V, the other k points lying in the interior of conv V. **max** \Delta (V) denotes the minimum area of a triangle with vertices in V, and the maximum is taken over all such sets V.

**Reviewer: ** B.Kind (Bochum)

**Classif.: ** * 52A10 Convex sets in 2 dimensions (including convex curves)

52A40 Geometric inequalities, etc. (convex geometry)

**Keywords: ** triangles in convex polygons

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