English

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 Z2\Z^2. 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}
}