Resources
Klara Mundilova, and Oliver Gross
Preprint: https://doi.org/10.48550/arXiv.2602.22164
[Preprint] [Code]
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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 Limacon trisectrices. |
Resources |
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(Semi-)Invariant Curves From Centers of Triangle Families Klara Mundilova, and Oliver Gross Preprint: https://doi.org/10.48550/arXiv.2602.22164 [Preprint] [Code] |
Acknowledgement |
| We thank the current and past members of the Geometric Computing Laboratory at EPFL, in particular Prof. Mark Pauly, for insightful discussions. Klara Mundilova was supported by the Swiss Government Excellence Scholarship of the Swiss Confederation. |