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...
- terms horosphere and horocycle are due to Lobachevsky, who established various results showing that the geometry of horocycles and the horosphere in...
- 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...
- +\infty )} [clarification needed] and the arclength along this horocycle. Draw the horocycle hO through the origin centered at the ideal point Ω {\displaystyle...
- 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...
- tangent configurations in hyperbolic geometry including hypercycles and horocycles, if k j {\displaystyle k_{j}} is taken to be the reciprocal of the stereographic...
- and information theory. He has published contributions in the theory of horocycle flows and entropy. Marcus has written over seventy research papers, some...
- mathematics, ergodic flows occur in geometry, through the geodesic and horocycle flows of closed hyperbolic surfaces. Both of these examples have been...
- vertical line which models its axis, but at an acute or obtuse angle. A horocycle (a curve whose normals all converge asymptotically in the same direction...
- regular apeirogons around each vertex. Each apeirogon is inscribed in a horocycle. The order-2 apeirogonal tiling represents an infinite dihedron in the...