hyperparallel

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.

Adjective

  1. 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.
    • Two hyperparallel lines have one and only one common perpendicular. - 1995, Howard Eves, College Geometry, page 246:
    • 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. - 2012, G. E. Martin, The Foundations of Geometry and the Non-Euclidean...
    • 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. - 2018, Karol Borsuk, Wanda...

Origin

From hyper- + parallel.