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arXiv · 2604.25956

Lattice triangles whose centers are lattice points

Christian Aebi·Grant Cairns
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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 $\ell=6 $ or $\ell\ge 8$. Analogous results are obtained for the circumcenter and the centroid, and the results are contrasted with those for obtuse and right triangles.

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Christian Aebi, Grant Cairns. 2026-04-27. Lattice triangles whose centers are lattice points. https://arxiv.org/abs/2604.25956

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