Abstract
By the theory of elliptic curves, we show that there are infinitely many integral right triangle-perpendicular quadrilateral, integral isosceles triangle-perpendicular quadrilateral, and Heron triangle-perpendicular quadrilateral pairs with a common area and a common perimeter. Moreover, for the elliptic curve associated to integral isosceles triangle and integral perpendicular quadrilateral pairs, we present several subfamilies of rank $\geq 4$, and show the existence of infinitely many elliptic curves of rank $\geq 5$, parameterized by the points of an elliptic curve of positive rank.
Citation
Arman Shamsi Zargar. Yong Zhang. "Integral triangles and perpendicular quadrilateral pairs with a common area and a common perimeter." Funct. Approx. Comment. Math. 63 (2) 165 - 180, December 2020. https://doi.org/10.7169/facm/1842
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