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...
- 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...
- 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...
- 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...
- 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...
- 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...
- of the sphere it projects generalized circles (geodesics, hypercycles, horocycles, and circles) in the hyperbolic plane to generalized circles (lines or...
- regular apeirogons around each vertex. Each apeirogon is inscribed in a horocycle. The order-2 apeirogonal tiling represents an infinite dihedron in the...
- and information theory. He has published contributions in the theory of horocycle flows and entropy. Marcus has written over seventy research papers, some...