Integral isosceles triangle-parallelogram and Heron triangle-rhombus pairs with a common area and common perimeter

JOURNAL OF NUMBER THEORY

卷:180

Article

Das, Pradeep¹  Juyal, Abhishek²  Moody, Dustin³ 

[1] HBNI, Harish Chandra Res Inst, Allahabad, Uttar Pradesh, India

[2] Motilal Nehru Natl Inst Technol, Dept Math, Allahabad 211004, Uttar Pradesh, India

[3] Natl Inst Stand & Technol, Comp Secur Div, Gaithersburg, MD 20899 USA

关键词: Elliptic curve;    Isosceles triangle;    Heron triangle;    Parallelogram;    Rhombus;    Common area;    Common perimeter;   

DOI  :  10.1016/j.jnt.2017.04.009

来源: Elsevier

【 摘 要 】

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. Published by Elsevier Inc.

【 授权许可】

Free