Das, P.
, Juyal, A.
and Moody, D.
(2017),
Integral Isosceles Triangle-Parallelogram and Heron triangle-Rhombus Pairs with a Common Area and Common Perimeter, Journal of Number Theory, [online], https://doi.org/10.1016/j.jnt.2017.04.009, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=923308
(Accessed October 13, 2024)
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Integral Isosceles Triangle-Parallelogram and Heron triangle-Rhombus Pairs with a Common Area and Common Perimeter
Published
Author(s)
Pradeep Das, Abhishek Juyal,
Abstract
In this paper we show that there are in nitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are in nitely many Heron triangles and integer rhombuses with common area and common perimeter. As a corollary, we show there does not exist any Heron triangle and integer square which have a common area and common perimeter.Citation
Journal of Number Theory
Volume
180
Pub Type
Journals
Download Paper
Keywords
Elliptic Curve, Isosceles Triangle, Heron Triangle, Rhombus, Parallelogram
Citation
Issues
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Created June 5, 2017, Updated October 12, 2021