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

被引：10

作者：

Das, Pradeep ^{[1
]}

Juyal, Abhishek ^{[2
]}

Moody, Dustin ^{[3
]}

机构：

[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

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 180卷

关键词：

Elliptic curve; Isosceles triangle; Heron triangle; Parallelogram; Rhombus; Common area; Common perimeter; ELLIPTIC-CURVES;

D O I：

10.1016/j.jnt.2017.04.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：208 / 218

页数：11

共 12 条

[1]

[Anonymous], 1994, GRAD TEXTS MATH

[2] Triangle-rectangle pairs with a common area and a common perimeter [J].

Bremner, Andrew ;

Guy, Richard K. .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2006, 2 (02) :217-223

[3]

Bremner A, 2006, ANN MATH INFORM, V33, P15

[4]

Chern S., 2016, FORUM GEOM, V16, P25

[5]

Coins E.H., 2006, ROCKY MOUNTAIN J MAT, V36, P1511

[6] ELLIPTIC CURVES COMING FROM HERON TRIANGLES [J].

Dujella, Andrej ;

Peral, Juan Carlos .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2014, 44 (04) :1145-1160

[7] MY FAVORITE ELLIPTIC CURVE - A TALE OF 2 TYPES OF TRIANGLES [J].

GUY, RK .

AMERICAN MATHEMATICAL MONTHLY, 1995, 102 (09) :771-781

[8]

Izadi F., 2017, ROCKY MOUNT IN PRESS

[9] ELLIPTIC CURVES ARISING FROM BRAHMAGUPTA QUADRILATERALS [J].

Izadi, Farzali ;

Khoshnam, Foad ;

Moody, Dustin ;

Zargar, Arman Shamsi .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2014, 90 (01) :47-56

[10] Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples [J].

Naskrecki, Bartosz .

ACTA ARITHMETICA, 2013, 160 (02) :159-183

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