米克尔Möbius奇阶平面中的奇异斯坦纳链

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-04-01 DOI:10.1515/advgeom-2020-0035

N. Hungerbühler, Gideon Villiger

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引用次数: 1

摘要

摘要在欧几里得平面中，两个相交或相切的圆显然不带有有限的施泰纳圆链。我们证明了这种奇异的Steiner链存在于奇数阶的有限Miquelian Möbius平面中。我们得到了斯坦纳链存在、长度和数量的平面阶数和两个载流子圆的电容的显式条件。

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Exotic Steiner chains in Miquelian Möbius planes of odd order

Abstract In the Euclidean plane, two circles that intersect or are tangent clearly do not carry a finite Steiner chain of circles. We show that such exotic Steiner chains exist in finite Miquelian Möbius planes of odd order. We obtain explicit conditions in terms of the order of the plane and the capacitance of the two carrier circles for the existence, length, and number of Steiner chains.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.