Amicable Triangle and Rectangles on the Integer Lattice

Published 26 Mar 2025 in math.MG and math.CO | (2503.20458v1)

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 $\Z^2$. We show that there is one pair of amicable lattice triangles and five pairs of amicable lattice rectangles.

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