Two disjoint hyperbolic lines with four distinct ideal endpoints have a unique common perpendicular, and the segment of that perpendicular between them realizes their minimum distance. An upper-half-plane isometry can make the two lines concentric semicircles; their common perpendicular then becomes the imaginary axis.

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  1. Geodesic in the Poincare half-plane model
  2. Poincare half-plane model
  3. Hyperbolic geometry
  4. Geometry and topology
  5. Area of mathematics
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