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arXiv · 1702.06860

Spherical and hyperbolic conics

Ivan Izmestiev
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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.

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Ivan Izmestiev. 2017-02-22. Spherical and hyperbolic conics. https://arxiv.org/abs/1702.06860

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