The sad life of lattice triangles
Combinatorics
2026-03-02 v1
Abstract
This paper treats triangles in the plane whose vertices lie on the integer lattice, i.e., the vertices have integer coordinates. It shows that apart from trivial examples, the circumcenter, centroid and orthocenter of such triangles never all lie on the integer lattice. Several further observations are made concerning the circumcenter, centroid and orthocenter.
Cite
@article{arxiv.2602.23392,
title = {The sad life of lattice triangles},
author = {Christian Aebi and Grant Cairns},
journal= {arXiv preprint arXiv:2602.23392},
year = {2026}
}