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  "path": "/abs/2602.22164v1",
  "publishedAt": "2026-02-26T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Klara Mundilova",
    "Oliver Gross"
  ],
  "textContent": "**Authors:** Klara Mundilova, Oliver Gross\n\nWe 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"
}