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In hyperbolic geometry, a horocycle, 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.
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