horocycle
Sign in to saveAlso known as oricycle, limit circle
220px|right|thumb| A blue horocycle in the Poincaré disk model and some red normals. The normals converge asymptotically to the upper central [[ideal point.]]
In the Vinony graph
Vinony's link graph records 35 inbound references to horocycle, and connects out to circle, International Standard Book Number and infinity.
Vinony files it under Curves and Hyperbolic geometry.
Vinony links it to 8 Wikipedia language editions.
Wikidata facts
- Subclass of
- curve
- Image
- Horocycle normals.svg
Show 1 more fact
- maintained by WikiProject
- WikiProject Mathematics
Sources (1)
via Wikidata · CC0
~9 min read
Encyclopedic overview
13 sectionsContents
- Properties
- Properties similar to those of Euclidean circles
- Other properties
- Horocycles in a hyperbolic plane with standardized Gaussian curvature
- Representations in models of hyperbolic geometry
- Poincaré disk model
- Poincaré half-plane model
- Hyperboloid model
- Metric
- Horocycle flow
- See also
- References
- Further reading
220px|right|thumb| A blue horocycle in the Poincaré disk model and some red normals. The normals converge asymptotically to the upper central [[ideal point.]]
In hyperbolic geometry, a horocycle (from Greek roots meaning "boundary circle"), sometimes called an oricycle or limit circle, is a curve of constant curvature where all the perpendicular geodesics (normals) through a point on a horocycle are limiting parallel, and all converge asymptotically to a single ideal point called the centre of the horocycle. In some models of hyperbolic geometry, it looks like the two "ends" of a horocycle get closer and closer to each other and closer to its centre, but this is not true; the two "ends" of a horocycle get further and further away from each other and stay at an infinite distance off its centre. A horosphere is the 3-dimensional version of a horocycle.
Excerpted from Wikipedia’s “horocycle” article, available under the CC BY-SA 4.0 licence.