hyperparallel

English

Etymology

hyper- +‎ parallel

Adjective

hyperparallel (not comparable)

1. (geometry) In hyperbolic geometry, lines that do not intersect in a common point in the plane and do not intersect at a common limit point at infinity, but rather, occur outside the limit set by parallel lines which intersect at infinity.
   • 1995, Howard Eves, College Geometry, page 246:

     Two hyperparallel lines have one and only one common perpendicular.

   • 2012, G. E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, page 357:

     Let l and m be two hyperparallel lines. All the transversals to l and m that form congruent corresponding angles with l and m lie in a pencil.

   • 2018, Karol Borsuk, Wanda Szmielew, Foundations of Geometry, page 292:

     In order that two distinct lines K and L be hyperparallel it is necessary and sufficient that they lie in one plane and that there exists a line M intersecting both of them perpendicularly.