A Result About the Density of Iterated Line Intersections in the Plane

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dc.creatorHillar, Christopher J.
dc.creatorRhea, Darren L.
dc.date2005-07-22
dc.date2005-07-25
dc.date.accessioned2026-07-07T05:21:56Z
dc.date.available2026-07-07T05:21:56Z
dc.descriptionLet $S$ be a finite set of points in the plane and let $\mathcal{T}(S)$ 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 $\mathbb Q^2$ through iteration of $\mathcal{T}$.
dc.description10 pages, 8 figures (low-res for the arXiv), Computational Geometry: Theory and Applications
dc.identifierhttps://arxiv.org/abs/math/0507472
dc.identifierhttp://arxiv.org/abs/math/0507472
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75874
dc.subjectMetric Geometry
dc.subject52C30, 52C10
dc.titleA Result About the Density of Iterated Line Intersections in the Plane
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