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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 L and a point P not on L, we can construct a hypercycle by taking all points Q on the same side of L as P, with perpendicular distance to L equal to that of P. The line L is called the ''axis'', ''center'', or ''base line'' of the hypercycle. The orthogonal segments from each point to L 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. == Properties similar to that of Euclidean lines == Hypercycles in hyperbolic geometry have some properties similar to those of lines in Euclidean geometry: * In a plane, given a line and a point not on it, there is only one hypercycle of that of the given line (compare with Playfair's axiom for Euclidean geometry). * No three points of a hypercycle are on a circle. * A hypercycle is symmetrical to each line perpendicular to it. (Reflecting a hypercycle in a line perpendicular to the hypercycle results in the same hypercycle.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hypercycle (hyperbolic geometry)」の詳細全文を読む スポンサード リンク
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