(Semi-)Invariant Curves from Centers of Triangle Families
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911468717342720 |
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| author | Mundilova, Klara Gross, Oliver |
| author_facet | Mundilova, Klara Gross, Oliver |
| contents | We study curves obtained by tracing triangle centers within special families of triangles, focusing on centers and families that yield (semi-)invariant triangle curves, meaning that varying the initial triangle changes the loci only by an affine transformation. We identify four two-parameter families of triangle centers that are semi-invariant and determine which are invariant, in the sense that the resulting curves for different initial triangles are related by a similarity transformation. We further observe that these centers, when combined with the aliquot triangle family, yield sheared Maclaurin trisectrices, whereas the nedian triangle family yields Limaçon trisectrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | (Semi-)Invariant Curves from Centers of Triangle Families Mundilova, Klara Gross, Oliver Metric Geometry Computational Geometry We study curves obtained by tracing triangle centers within special families of triangles, focusing on centers and families that yield (semi-)invariant triangle curves, meaning that varying the initial triangle changes the loci only by an affine transformation. We identify four two-parameter families of triangle centers that are semi-invariant and determine which are invariant, in the sense that the resulting curves for different initial triangles are related by a similarity transformation. We further observe that these centers, when combined with the aliquot triangle family, yield sheared Maclaurin trisectrices, whereas the nedian triangle family yields Limaçon trisectrices. |
| title | (Semi-)Invariant Curves from Centers of Triangle Families |
| topic | Metric Geometry Computational Geometry |
| url | https://arxiv.org/abs/2602.22164 |