Amicable Triangle and Rectangles on the Integer Lattice
Metric Geometry
2025-03-27 v1 Combinatorics
Abstract
Two polygons are amicable if the perimeter of one is equal to the area of the other and vice versa. A polygon is a lattice polygon if its vertices are on the integer lattice . We show that there is one pair of amicable lattice triangles and five pairs of amicable lattice rectangles.
Keywords
Cite
@article{arxiv.2503.20458,
title = {Amicable Triangle and Rectangles on the Integer Lattice},
author = {Iwan Praton and Weiran Zeng},
journal= {arXiv preprint arXiv:2503.20458},
year = {2025}
}