Heron quadrilaterals with sides in arithmetic or geometric progression

被引：7

作者：

Buchholz, RH

MacDougall, JA

机构：

[1] Dept Def, Kingston, ACT 2605, Australia

[2] Univ Newcastle, Dept Math, Callaghan, NSW 2308, Australia

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 1999年 / 59卷 / 02期

关键词：

D O I：

10.1017/S0004972700032883

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterisation is given for the infinite family of triangles with sides in arithmetic progression. We show that there are no triangles with sides in geometric progression. We also show that apart from the square there are no cyclic quadrilaterals whose sides form either a geometric or an arithmetic progression. The solution of both quadrilateral cases involves searching for rational points on certain elliptic curves.

引用

页码：263 / 269

页数：7