English

Lattice triangles whose centers are lattice points

General Mathematics 2026-04-30 v1

Abstract

We show that for an integer \ell, there exists an acute integer lattice triangle of lattice perimeter \ell such that its orthocenter is an integer lattice point, if and only if =6\ell=6 or 8\ell\ge 8. Analogous results are obtained for the circumcenter and the centroid, and the results are contrasted with those for obtuse and right triangles.

Keywords

Cite

@article{arxiv.2604.25956,
  title  = {Lattice triangles whose centers are lattice points},
  author = {Christian Aebi and Grant Cairns},
  journal= {arXiv preprint arXiv:2604.25956},
  year   = {2026}
}
R2 v1 2026-07-01T12:39:48.353Z