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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