On the relative lengths of the sides of convex polygons
Zhanjun Su, Рен Динг · Advances in Geometry · 2008
Abstract Doliwka and Lassak proved that if n ≤ 5 then every convex n-gon has a relatively short side and a relatively long side. In this paper we prove that this is true for n ≤ 5 only. More precisely, for any n ≥ 6, there exist n-gons without any relatively short sides.