Definition of Horocycles. Meaning of Horocycles. Synonyms of Horocycles

- perpendicular to every concentric horocycle. Through every pair of points there are 2 horocycles. The centres of the horocycles are the ideal points of the...
- 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...
- there are 4 distinct types of generalized circles or cycles: circles, horocycles, hypercycles, and geodesics (or "hyperbolic lines"). In the Poincaré disk...
- 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)...
- 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...
- 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...
- circles can be interpreted as horocycles. In hyperbolic geometry any two horocycles are congruent. When these horocycles are cir****scribed by apeirogons...
- impossible in Euclidean geometry, like infinite trees, equidistants and horocycles, and straight lines which never cross. There is also one land that relies...
- of the sphere it projects generalized circles (geodesics, hypercycles, horocycles, and circles) in the hyperbolic plane to generalized circles (lines or...
- covering map is periodic in the x direction of period 2π, and takes the horocycles y = c to the meridians of the pseudosphere and the vertical geodesics...