Abstract
Let S be a set of at least five points in the plane, not all on a line. Suppose that for any three points \({a,b,c\in S}\) the nine-point center of triangle abc also belongs to S. We show that S must be dense in the plane. We also consider several problems about partitioning the plane into two sets containing their triangle centers.
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More From: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
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