Hypercycle (geometry)

Article summary

showing the hypercycle that is determined by the straight line (termed straight because it cuts the horizon at right angles) and point In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis). Given a straight line and a point not on , one can construct a hypercycle by taking all points on the same side of as , with perpendicular distance to equal to that of . The line is called the axis, center, or base line of the hypercycle. The lines perpendicular to , which are also perpendicular to the hypercycle, are called the normals of the hypercycle. The segments of the normals between and the hypercycle are called the radii. Their common length is called the distance or radius of the hypercycle. The hypercycles through a given point that share a tangent through that point converge towards a horocycle as their distances go towards infinity.

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