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

Christopher J. Hillar·Darren L. Rhea
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Abstract

Let $S$ 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 $\mathcal{T}$.

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Christopher J. Hillar, Darren L. Rhea. 2005-07-25. A Result About the Density of Iterated Line Intersections in the Plane. https://arxiv.org/abs/math/0507472

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