Elementary Constructions for Conics in Hyperbolic and Elliptic Planes

@inproceedings{Weiss2016ElementaryCF,
  title={Elementary Constructions for Conics in Hyperbolic and Elliptic Planes},
  author={Guenter Weiss},
  year={2016}
}
In the Euclidean plane there are well-known constructions of points and tangents of e.g. an ellipse c based on the given axes of c, which make use of the Apollonius definition of c via its focal points or via two perspective affinities (de la Hire’s construction). Even there is no parallel relation neither in a hyperbolic plane nor in an elliptic plane it is still possible to modify many of the elementary geometric constructions for conics, such that they also hold for those (regular) non… CONTINUE READING