Point sets containing their triangle centers (Q664203)
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scientific article; zbMATH DE number 6010040
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Point sets containing their triangle centers |
scientific article; zbMATH DE number 6010040 |
Statements
Point sets containing their triangle centers (English)
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29 February 2012
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The structure of subsets \(S\) of the Euclidean plane that may be generated according to some prescribed geometric rule is studied. One of the prescribed rules asks that the nine-point center of each triangle having the vertices in \(S\) belongs to \(S\) as well. The author shows that such a set \(S\) is dense in the plane. The cases of orthocenters, circumcenter and centroid are also investigated.
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dense point set
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nine-point center
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triangle centers
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iterated process
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