Lattice triangles whose centers are lattice points
General Mathematics
2026-04-30 v1
Abstract
We show that for an integer , there exists an acute integer lattice triangle of lattice perimeter such that its orthocenter is an integer lattice point, if and only if or . 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}
}