- Working Paper
We investigate Steiner's Porism in finite Miquelian Möbius planes constructed over the pair of finite fields GF(pm) and GF(p2m), for p an odd prime and m≥1. Properties of common tangent circles for two given concentric circles are discussed and with that, a finite version of Steiner's Porism for concentric circles is stated and proved. We formulate conditions on the length of a Steiner chain by using the quadratic residue theorem in GF(pm). These results are then generalized to an arbitrary pair of non-intersecting circles by introducing the notion of capacitance, which turns out to be invariant under Möbius transformations. Finally, the results are compared with the situation in the classical Euclidean plane. Show more
Journal / seriesarXiv
Pages / Article No.
SubjectFinite Möbius planes; Steiner^s Theorem; Steiner chains; Capacitance
Organisational unit03874 - Hungerbühler, Norbert / Hungerbühler, Norbert
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