Published: November 1, 2017
Citation: Journal of Number Theory vol. 180, (November 2017) pp. 208-218
Author(s)
Pradeep Das (Harish-Chandra Research Institute), Abhishek Juyal (Motilal Nehru National Institute of Technology), Dustin Moody (NIST)
In this paper we show that there are infinitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are infinitely 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.
In this paper we show that there are infinitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are infinitely many Heron triangles and integer rhombuses with common area and common perimeter. As a...
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In this paper we show that there are infinitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are infinitely 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.
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Keywords
Elliptic curve; Isosceles triangle; Heron triangle; Parallelogram; Rhombus; Common area; Common perimeter
Control Families
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