page_title: Hypercycle (geometry)
section_title: References
hierarchical_section_title: Hypercycle (geometry) / References
caption_attribution_description: English: en:Tritetragonal_tiling image, centered on edge
context_page_description: In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line.
  Given a straight line L and a point P not on L, one 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 lines perpendicular to the axis, which is also perpendicular to the hypercycle are called the normals of the hypercycle.
  The segments of the normal between the axis, 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.
context_section_description: Martin, George E. (1986). The foundations of geometry and the non-euclidean plane (1., corr. Springer ed.). New York: Springer-Verlag. p. 371. ISBN 3-540-90694-0.
  Smogorzhevsky, A.S. (1982). Lobachevskian  geometry. Moscow: Mir. p. 68.
  Martin Gardner, Non-Euclidean Geometry, Chapter 4 of The Colossal Book of Mathematics, W. W. Norton & Company, 2001, ISBN 978-0-393-02023-6
  M. J. Greenberg, Euclidean and Non-Euclidean Geometries: Development and History, 3rd edition, W. H. Freeman, 1994.
  George E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, Springer-Verlag, 1975.
  David C. Royster, Neutral and Non-Euclidean Geometries.
caption: The alternated octagonal tiling, in a Poincaré disk model, can be seen with edge sequences that follow hypercycles.
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