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.

中文翻译：

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奇数阶MiquelianMöbius飞机上的奇异Steiner链

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Steiner圆链。我们证明了这种奇异的Steiner链存在于奇数阶的有限MiquelianMöbius平面中。我们根据Steiner链的存在，长度和数量的平面顺序和两个载流子圆的电容来获得明确的条件。