TRIANGLE-RECTANGLE PAIRS WITH A COMMON AREA AND A COMMON PERIMETER-Reference-Cited by-同舟云学术

TRIANGLE-RECTANGLE PAIRS WITH A COMMON AREA AND A COMMON PERIMETER

Published:2006-06 Issue:02 Volume:02 Page:217-223
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BREMNER ANDREW¹,GUY RICHARD K.²

Affiliation:

1. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, USA

2. Department of Mathematics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada

Abstract

We solve a problem of Bill Sands, to find pairs of Heron triangles and rectangles, such as (5,5,6) & [2 × 6] or (13,20,21) & [6 × 21] which have a common area and a common perimeter. The original question was posed for right-angled triangles, but there are no nondegenerate such. There are infinitely many isosceles triangles and these have been exhibited by Guy. Here we solve the general problem; the triangle-rectangle pairs are parametrized by a family of elliptic curves.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042106000504

Reference4 articles.

1. Compact Complex Surfaces

2. My Favorite Elliptic Curve: A Tale of Two Types of Triangles

3. On elliptic modular surfaces

Cited by 12 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A note on tangential quadrilaterals;Quaestiones Mathematicae;2024-09-02

2. Pairs of Heron and right triangles with a common area and a common perimeter;Publicationes Mathematicae Debrecen;2022-04-01

3. On an elliptic curve involving pairs of triangles and special quadrilaterals;International Journal of Number Theory;2022-02-25

4. Richard Kenneth Guy, 1916–2020;Bulletin of the London Mathematical Society;2022-02

5. Rational triangle pairs and cyclic quadrilateral pairs with areas and perimeters in certain proportions;Functiones et Approximatio Commentarii Mathematici;2021-09-13