Exotic Steiner Chains in Miquelian Möbius Planes

Thursday, 15 November, 2018

Published in: 

arXiv:1811.06201

In the Euclidean plane, two intersecting circles or two circles which are tangent to each other clearly do not carry a finite Steiner chain. However, in this paper we will show that such exotic Steiner chains exist in finite Miquelian Möbius planes of odd order. We state and prove explicit conditions in terms of the order of the plane and the capacitance of the two carrier circles C1 and C2 for the existence, length, and number of Steiner chains carried by C1 and C2.

Author(s): 

Norbert Hungerbühler
Gideon Villiger