On the Density of Iterated Line Segment Intersections
| dc.creator | Gruene, Ansgar | |
| dc.creator | Sarvestani, Sanaz Kamali | |
| dc.date | 2005-12-07 | |
| dc.date | 2007-07-02 | |
| dc.date.accessioned | 2026-07-07T08:13:13Z | |
| dc.date.available | 2026-07-07T08:13:13Z | |
| dc.description | 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. | |
| dc.description | 20 pages, 17 figures, revised version, still based on Technical Report 004 | |
| dc.identifier | https://arxiv.org/abs/math/0512158 | |
| dc.identifier | http://arxiv.org/abs/math/0512158 | |
| dc.identifier | Technical Report 004, Department of Computer Science I, University of Bonn, Germany, 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132723 | |
| dc.subject | Metric Geometry | |
| dc.subject | 51M04; 14N05 | |
| dc.title | On the Density of Iterated Line Segment Intersections | |
| dc.type | text |