Heron triangle and rhombus pairs with a common area and a common perimeter

Yong Zhang; Junyao Peng

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arXiv · 1707.00526

Heron triangle and rhombus pairs with a common area and a common perimeter

Yong Zhang·Junyao Peng

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Abstract

By Fermat's method, we show that there are infinitely many Heron triangle and $θ$-integral rhombus pairs with a common area and a common perimeter. Moreover, we prove that there does not exist any integral isosceles triangle and $θ$-integral rhombus pairs with a common area and a common perimeter.

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Yong Zhang, Junyao Peng. 2017-07-03. Heron triangle and rhombus pairs with a common area and a common perimeter. https://arxiv.org/abs/1707.00526

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