Unfolding simple chains inside circles

Abstract

It is an open problem to determined whether a polygonal chain can be straightened inside a confi ning region if its links are not allowed to cross. In this paper we propose a special case: whether a polygonal chain can be straightened inside a circle without allowing its links to cross. We prove that this is possible if the straightened confi guration can fi t within circle. Then we show that these simple chains have just one equivalence class of confi gurations.