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 {PPi} = 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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