caa a22 4500 445868988 CHVBK 20180411092529.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00605-010-0214-z doi (NATIONALLICENCE)springer-10.1007/s00605-010-0214-z 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 disk [Elektronische Daten] [Zsolt Lángi] A simple n-gon is a polygon with n edges with each vertex belonging to exactly two edges and every other point belonging to at most one edge. Brass etal. (Research Problems in Discrete Geometry, 2005) asked the following question: For n ≥5 odd, what is the maximum perimeter of a simple n-gon contained in a Euclidean unit disk? In 2009, Audet etal. (Discrete Comput Geom 41:208-215) answered this question, and showed that the optimal configuration is an isosceles triangle with a multiple edge, inscribed in the disk. In this note we give a shorter and simpler proof of their result, which we generalize also for hyperbolic disks, and for spherical disks of sufficiently small radii. Springer-Verlag, 2010 Isoperimetric problem nationallicence Simple polygon nationallicence Perimeter nationallicence Circumcircle nationallicence Monatshefte für Mathematik Springer Vienna 162/1(2011-01-01), 61-67 0026-9255 162:1<61 2011 162 605 https://doi.org/10.1007/s00605-010-0214-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0214-z 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- Monatshefte für Mathematik Springer Vienna 162/1(2011-01-01), 61-67 0026-9255 162:1<61 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 445868988 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer