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**Zentralblatt MATH**

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

**Zbl.No: ** 091.35402

**Autor: ** Erdös, Pál; Vincze, István

**Title: ** Über die Annäherung geschlossener, konvexer Kurven. (On the approach of closed convex curves) (In Hungarian. RU, German summary)

**Source: ** Mat. Lapok 9, 19-36 (1958).

**Review: ** The first part is an exposition of well known elementary facts on convex curves in the plane. Tschirnhaus curves (defined by **sum** \overline {PP_{i}} = c. Distance of two domains (or their boundary curves): the smallest r, such that the parallel domain at distance r of each domain contains the other one. The following theorem is new. An equilateral triangle is not the limit of Tschirnhaus curves. It is also remarked that there exists a convex curve containing a line segment which is the limit of Tschirnhaus curves. Uniqueness of an ellipse (domain) containing a given convex domain at minimal distance is proved.

**Reviewer: ** I.Fáry

**Classif.: ** * 52-99 Convex and discrete geometry

**Index Words: ** metric geometry, convex geometry, integral geometry

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