θ-triangle and ω-parallelogram pairs with common area and common perimeter

JOURNAL OF NUMBER THEORY

卷:202

Article

Lalin, Matilde¹  Ma, Xinchun² 

[1] Univ Montreal, Dept Math & Stat, CP 6128, Montreal, PQ H3C 3J7, Canada

[2] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China

关键词: theta-triangle;    omega-parallelogram;    Common area;    Common perimeter;    Elliptic curves;    Elliptic surfaces;   

DOI  :  10.1016/j.jnt.2019.02.002

来源: Elsevier

【 摘 要 】

We show that given a convex angle theta, there exist, except for finitely many exceptions, infinitely many pairs of integral theta-triangle and omega-parallelogram with common area and common perimeter satisfying that sine is a previously fixed rational multiple of sin theta. This is achieved by relating the problem to a family of elliptic curves. We also study the elliptic surfaces and the elliptic threefold that are obtained by varying one or two parameters. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free