Forum Geometricorum, 6 (2006) 139--147.

Abstract: We exhibit conditions that determine whether a set of 2n+1 lines are the medians of a (2n+1)-sided polygon. We describe how to regard certain collections of sets of medians as a linear subspace of related collections of sets of lines, and as a consequence, we show that every set of 2n+1 concurrent lines are the medians of some (2n+1)-sided polygon. Also, we derive conditions on n+1 points so that they can be consecutive vertices of a (2n+1)-sided polygon whose medians intersect at the origin. Each of these constructions demonstrates a procedure that generates (2n+4)-degree of freedom families of median-concurrent polygons. Furthermore, this number of degrees of freedom is maximal.

[ps file][pdf file]