On the Density of Iterated Line Segment Intersections

dc.creatorGruene, Ansgar
dc.creatorSarvestani, Sanaz Kamali
dc.date2005-12-07
dc.date2007-07-02
dc.date.accessioned2026-07-07T08:13:13Z
dc.date.available2026-07-07T08:13:13Z
dc.descriptionGiven 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.description20 pages, 17 figures, revised version, still based on Technical Report 004
dc.identifierhttps://arxiv.org/abs/math/0512158
dc.identifierhttp://arxiv.org/abs/math/0512158
dc.identifierTechnical Report 004, Department of Computer Science I, University of Bonn, Germany, 2005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132723
dc.subjectMetric Geometry
dc.subject51M04; 14N05
dc.titleOn the Density of Iterated Line Segment Intersections
dc.typetext

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