(Semi-)Invariant Curves from Centers of Triangle Families
Metric Geometry
2026-02-26 v1 Computational Geometry
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.
Cite
@article{arxiv.2602.22164,
title = {(Semi-)Invariant Curves from Centers of Triangle Families},
author = {Klara Mundilova and Oliver Gross},
journal= {arXiv preprint arXiv:2602.22164},
year = {2026}
}