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arXiv · 2602.22164

(Semi-)Invariant Curves from Centers of Triangle Families

Klara Mundilova·Oliver Gross
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Abstract

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 Lima\c{c}on trisectrices.

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Klara Mundilova, Oliver Gross. 2026-02-25. (Semi-)Invariant Curves from Centers of Triangle Families. https://arxiv.org/abs/2602.22164

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