Amicable Heron triangles
Iwan Praton, Nart Shalqini
TL;DR
This paper investigates pairs of Heron triangles with integer sides and areas, proving that there is only one such pair where the perimeter of one equals the area of the other, using elementary methods.
Contribution
The paper establishes the uniqueness of the only known pair of amicable Heron triangles through elementary techniques.
Findings
Only one pair of amicable Heron triangles exists.
The unique pair's properties are characterized.
Elementary methods suffice for the proof.
Abstract
A Heron triangle is a triangle whose side lengths and area are integers. Two Heron triangles are amicable if the perimeter of one is the area of the other. We show, using elementary techniques, that there is only one pair of amicable Heron triangles.
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Taxonomy
TopicsMathematics and Applications · Geometric and Algebraic Topology · Finite Group Theory Research