Three pairwise ultraparallel hyperbolic lines may have disjoint common perpendiculars or coincident ones. In the upper-half-plane model, three semicircles of radius centred at have mutually disjoint common perpendiculars. Three concentric semicircles instead have the same vertical common perpendicular. Thus pairwise ultraparallelism alone does not determine the incidence of their perpendiculars.

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  1. Common perpendicular of ultraparallel hyperbolic lines
  2. Geodesic in the Poincare half-plane model
  3. Poincare half-plane model
  4. Hyperbolic geometry
  5. Geometry and topology
  6. Area of mathematics
  7. Mathematics
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