On the Density of Iterated Line Segment Intersections
Metric Geometry
2007-07-02 v6
Abstract
Given S_1, a finite set of points in the plane, we define a sequence of point sets S_i as follows: With S_i already determined, let L_i be the set of all the line segments connecting pairs of points of the union of S_1,...,S_i, and let S_i+1 be the set of intersection points of those line segments in L_i, which cross but do not overlap. We show that with the exception of some starting configurations the set of all crossing points is dense in a particular subset of the plane with nonempty interior. This region is the intersection of all closed half planes which contain all but at most one point from S_1.
Keywords
Cite
@article{arxiv.math/0512158,
title = {On the Density of Iterated Line Segment Intersections},
author = {Ansgar Gruene and Sanaz Kamali Sarvestani},
journal= {arXiv preprint arXiv:math/0512158},
year = {2007}
}
Comments
20 pages, 17 figures, revised version, still based on Technical Report 004