Rational Right Triangles of a Given Area

被引：1

作者：

Chan, Stephanie ^{[1
]}

机构：

[1] UCL, Dept Math, Gower St, London WC1E 6BT, England

来源：

AMERICAN MATHEMATICAL MONTHLY | 2018年 / 125卷 / 08期

基金：

欧洲研究理事会;

关键词：

MSC: Primary 11A99; Secondary; 11G05;

D O I：

10.1080/00029890.2018.1495491

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Starting from any given rational-sided, right triangle, for example, the (3,4,5)-triangle with area 6, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show further that the set of all such triangles of a given area is finitely generated under our geometric construction. Such areas are known as congruent numbers and have a rich history in which all the results in this article have been proved and far more. Yet, as far as we can tell, this seems to be the first exploration using this kind of geometric technique.

引用

页码：689 / 703

页数：15