Abstract: | In this paper we explore pentagons that are affine images of the regular pentagon and the regular pentagram.
We obtain their characterizations in terms of two mild forms of regularity that deal with the notions of
medians for a pentagon and the natural requirement that they are concurrent. Using these characterizations we
show that there are various values involving the number 5 (thus related to the golden section) for which a careful
selection of division points on appropriate segments determined by any pentagon will result in a pentagon that is
the affine image of either a regular pentagon or a regular pentagram. |