神奇的二次曲线，它们的整数点和互补椭圆

Q4 Mathematics

Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi - Matematica Pub Date : 2021-01-01 DOI:10.47743/ANSTIM.2021.00010

M. Crasmareanu

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引用次数: 3

摘要

本文的目的是引入并研究由3 × 3幻方的对称矩阵所提供的一类二次曲线。该类依赖于三个实参数，这些实参数之间的各种关系给出了二次曲线的特殊子类。虽然没有神奇的圆，但我们发现了一个椭圆、一条抛物线和两条神奇的双曲线。整数点的搜索和一个复杂的方法也包括在内。我们还研究了一对互补椭圆，称为毕达哥拉斯椭圆。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Magic conics, their integer points and complementary ellipses

The aim of this paper is to introduce and study the class of conics provided by the symmetric matrices of the 3 × 3 magic squares. This class depends on three real parameters and various relationships between these parameters give special subclasses of conics. Although there are no magic circles we find an ellipse, a parabola and two hyperbolas of magic type. A search of integer points and a complex approach are also included. We study also a pair of complementary ellipses, called Pythagorean.

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来源期刊

Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi - Matematica MATHEMATICS-

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research and research-expository papers in all fields of mathematics.