Conformal Parametrisation of Loxodromes by Triples of Circles
Complex Variables
2019-11-07 v1 Group Theory
Abstract
We provide a parametrisation of a loxodrome by three specially arranged cycles. The parametrisation is covariant under fractional linear transformations of the complex plane and naturally encodes conformal properties of loxodromes. Selected geometrical examples illustrate the usage of parametrisation. Our work extends the set of objects in Lie sphere geometry---circle, lines and points---to the natural maximal conformally-invariant family, which also includes loxodromes.
Keywords
Cite
@article{arxiv.1802.01864,
title = {Conformal Parametrisation of Loxodromes by Triples of Circles},
author = {Vladimir V. Kisil and James Reid},
journal= {arXiv preprint arXiv:1802.01864},
year = {2019}
}
Comments
14 pages. 9 PDF in four figures, AMS-LaTex