Juyal, A.
and Moody, D.
(2022),
Pairs of Heron and right triangles with a common area and a common perimeter, Publicationes Mathematicae Debrecen, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=934575
(Accessed April 28, 2024)
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Pairs of Heron and right triangles with a common area and a common perimeter
Published
Author(s)
Abhishek Juyal,
Abstract
A Heron triangle is one in which the side lengths and area are integers. An integral right triangle is an example of a Heron triangle. In this paper, we show that there are infinitely many pairs of integral right triangles and Heron triangles with a common area and common perimeter, continuing a line of similar results with other pairs of geometric shapes. This result is established using the theory of elliptic curves.Citation
Publicationes Mathematicae Debrecen
Volume
100
Pub Type
Journals
Download Paper
Keywords
elliptic curve, right triangle, Heron triangle, parallelogram, common area, common perimeter
Citation
Created May 23, 2022, Updated November 29, 2022