Spherical and hyperbolic conics
Metric Geometry
2017-02-23 v1
Abstract
This is a survey of metric properties of non-Euclidean conics, mainly based on works of Chasles and Story. A spherical conic is the intersection of the sphere with a quadratic cone; similarly, a hyperbolic conic is the intersection of the Beltrami-Cayley-Klein disk with an affine conic. Non-Euclidean conics have metric properties similar to those of Euclidean conics, and even more due to the polarity that works here better than in the Euclidean plane.
Keywords
Cite
@article{arxiv.1702.06860,
title = {Spherical and hyperbolic conics},
author = {Ivan Izmestiev},
journal= {arXiv preprint arXiv:1702.06860},
year = {2017}
}
Comments
50 pages, 37 figures