关于两个椭圆体的阿波罗尼奥斯曲面

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-06-27 DOI:10.1007/s00010-024-01101-0

Attila Végh

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引用次数: 0

摘要

阿波罗尼奥斯把圆定义为与两个给定点的距离具有给定比率 \(\mu \)的点的集合，其中比率不等于一。在更一般的意义上，考虑两个 0 对称、有界、凸体 K 和 \(K'\)，它们定义了两个规范。它们的单位球是 K 和 \(K'\)。阿波罗尼奥斯曲面被定义为与上述准则相关的、与体 K 和（K'\）的中心等距离的点的集合。在本文中，我们证明了两个椭圆体的阿波罗尼奥斯曲面是一个二次曲面。我们还研究了这个曲面变成球面的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On surface of Apollonius of two ellipsoids

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On surface of Apollonius of two ellipsoids

Apollonius defined the circle as the set of points that have a given ratio \(\mu \) of distances from two given points, where the ratio is not equal to one. In a more general sense, consider two 0-symmetric, bounded, convex bodies K and \(K'\), which define two norms. Their unit balls are K and \(K'\). The surface of Apollonius is defined as the set of points equidistant from the centres of bodies K and \(K'\) with respect to the aforementioned norms. In this paper we demonstrate that the surface of Apollonius of two ellipsoids is a quadratic surface. We also examine the circumstances under which this surface becomes a sphere.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.