Matthew Hudelson, Concurrent medains of (2n+1)-gons,
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.
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