  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
asked the following question: For $n \geq 5$ odd, what is the maximum perimeter
of a simple $n$-gon contained in a Euclidean unit disk?
  In 2009, Audet, Hansen and Messine 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.
