2002 (Publication #90)
Midpoint Polygons Revisited on the Internet (with Stephen Canon, et. al.)
accepted for publication in the NCTM electronic journal "OnMath", under revision.
View the website for this article
In the Spring semester of 1999, Professor Thomas Banchoff of Brown University presented the midpoint polygons problem to the students in his Fundamental Problems of Geometry course, Math 104. He mentioned Rose Mary Zbiek's article, and challenged his students to go beyond the earlier investigations. The students discussed the midpoint problem on the interactive course webpage, as well as in class, and came up with a number of new results, including an explicit general formula for the area ratio. This paper is based on the results of that discussion.
In this paper we solve the area ratio problem for all planar polygons, including non-convex and self-intersecting polygons.