naa a22 4500 510736920 CHVBK 20180411092755.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s13366-012-0120-8 doi (NATIONALLICENCE)springer-10.1007/s13366-012-0120-8 Lángi Zsolt Department of Geometry, Budapest University of Technology, Egry József u. 1, 1111, Budapest, Hungary aut On the perimeters of simple polygons contained in a plane convex body [Elektronische Daten] [Zsolt Lángi] A simple n-gon is a polygon with n edges such that each vertex belongs to exactly two edges and every other point belongs to at most one edge. Brass etal. (Research Problems in Discrete Geometry, 2005, Problem 3, p. 437) asked the following question: For n ≥ 5 odd, what is the maximum perimeter of a simple n-gon contained in a Euclidean unit disk? Audet etal. (Discrete Comput Geom 41:208-215, 2009) answered this question, and showed that the supremum is the perimeter of an isosceles triangle inscribed in the disk, with an edge of multiplicity n−2. Lángi (Monatsh Math 162:61-67, 2011) generalized their result for polygons contained in a hyperbolic disk. In this note we find the supremum of the perimeters of simple n-gons contained in an arbitrary convex body in the Euclidean or in the hyperbolic plane. The Managing Editors, 2012 Isoperimetric problem nationallicence Simple polygon nationallicence Perimeter nationallicence Circumcircle nationallicence Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 643-649 0138-4821 54:2<643 2013 54 13366 https://doi.org/10.1007/s13366-012-0120-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0120-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lángi Zsolt Department of Geometry, Budapest University of Technology, Egry József u. 1, 1111, Budapest, Hungary aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer Berlin Heidelberg 54/2(2013-10-01), 643-649 0138-4821 54:2<643 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445868988 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer