Homemath.MGarXiv:2605.29905

On Ceva's and Menelaus's Theorems for a M\"obius triangle

math.MG2026-05v1license

Abstract

We generalize the classical Ceva's and Menelaus's theorems to curvilinear triangles bounded by circular arcs. We introduce trilinear coordinates associated with such triangles and develop several geometric constructions. In particular, for any proper M\"obius triangle we define the incenter, excenters, and orthocenter.

Comments: 35 pages, 18 figures

Cite

@article{arxiv.2605.29905,
  title  = {On Ceva's and Menelaus's Theorems for a M\"obius triangle},
  author = {Ivan Livinsky},
  journal= {arXiv preprint arXiv:2605.29905},
  year   = {2026}
}