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

Yong Zhang; Junyao Peng

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

Number Theory 2017-07-04 v1

Authors: Yong Zhang , Junyao Peng

Abstract

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

Keywords

heron triangle rhombus common area common perimeter fermat's method theta-integral isosceles triangle diophantine equations

Cite

@article{arxiv.1707.00526,
  title  = {Heron triangle and rhombus pairs with a common area and a common perimeter},
  author = {Yong Zhang and Junyao Peng},
  journal= {arXiv preprint arXiv:1707.00526},
  year   = {2017}
}

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5 pages

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

Abstract

Keywords

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