A result about the density of iterated line intersections in the plane

Let S be a finite set of points in the plane and let T (S) be the set of intersection points between pairs of lines passing through any two points in S. We characterize all configurations of points S such that iteration of the above operation produces a dense set. We also discuss partial results on the characterization of those finite point-sets with rational coordinates that generate all of Q2 through iteration of T .

• Type: Journal
• Year: 2006
• Where: COMGEO
• Authors: Christopher J. Hillar, Darren L. Rhea
• Keywords: Applied Computing, COMGEO 2006, Configurations, Intersection Points, Iteration