Amicable Heronian Parallelograms
Iwan Praton, Weiran Zeng
TL;DR
This paper investigates pairs of Heronian parallelograms with integer sides and areas, establishing the existence of infinitely many amicable pairs and providing conditions for their formation.
Contribution
It proves the existence of infinitely many amicable Heronian parallelogram pairs and characterizes the conditions under which a Heronian parallelogram can be part of such a pair.
Findings
Infinitely many amicable Heronian parallelogram pairs exist.
Necessary and sufficient conditions for a Heronian parallelogram to be amicable.
Characterization of amicable pairs based on geometric properties.
Abstract
A convex polygon is Heronian if its side lengths and its area are integers. Two polygons are amicable if the area of one is equal to the perimeter of the other, and vice versa. We show that there are infinitely many pairs of amicable Heronian parallelograms, and we give necessary and sufficient conditions for a Heronian parallelogram to be part of an amicable pair.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Digital Image Processing Techniques · Computational Geometry and Mesh Generation