Definition of Horocycle. Meaning of Horocycle. Synonyms of Horocycle

- In hyperbolic geometry, a horocycle (from Gr**** roots meaning "boundary circle"), sometimes called an oricycle or limit circle, is a curve of constant...
- ideal point, the centre of the horocycle). Through every pair of points there are two horocycles. The centres of the horocycles are the ideal points of the...
- boundary circle is not part of the horocycle. It is an ideal point and is the hyperbolic center of the horocycle. It is also the point to which all the...
- to some given horocycle. These numbers are the hyperbolic distance x h {\displaystyle x_{h}} from P {\displaystyle P} to the horocycle, and the (signed)...
- terms horosphere and horocycle are due to Lobachevsky, who established various results showing that the geometry of horocycles and the horosphere in...
- Ratner around 1990. The theorems grew out of Ratner's earlier work on horocycle flows. The study of the dynamics of unipotent flows pla**** a decisive...
- arcs of horocycles. The choice of log ⁡ 2 {\displaystyle \log 2} as the distance between the two horocycles causes one of the two arcs of horocycles (the...
- The half pseudosphere of curvature −1 is covered by the interior of a horocycle. In the Poincaré half-plane model one convenient choice is the portion...
- boundary circle are not distorted. All other circles are distorted, as are horocycles and hypercycles Chords that meet on the boundary circle are limiting parallel...
- of the sphere it projects generalized circles (geodesics, hypercycles, horocycles, and circles) in the hyperbolic plane to generalized circles (lines or...