Amicable Lattice Rhombuses are Amicable
Bohdan Biekietov, Iwan Praton, Weiran Zeng
TL;DR
The paper proves that amicable pairs of lattice rhombuses are necessarily equable, linking two geometric properties in lattice polygons.
Contribution
It establishes that amicable lattice rhombuses must be equable, revealing a specific geometric constraint for these polygons.
Findings
Amicable lattice rhombuses are always equable.
The result connects amicability with equability in lattice polygons.
This provides a new characterization of lattice rhombuses.
Abstract
A polygon is equable if its area is equal to its perimeter. A pair of polygons is an amicable pair if the area of the first is equal to the perimeter of the second, and vice versa. A polygon is a lattice polygon if its vertices lie on the integer lattice. We show that amicable lattice rhombuses are actually equable.
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