Limiting parallel
In neutral geometry, as there may be many lines parallel to a given line l at a point P, one parallel may be closer to l than all others. Thus it is useful to make a new definition concerning parallels in neutral geometry. The relation of limiting parallel for rays is an equivalence relation, which includes the equivalence relation of being coterminal.
Limiting parallels may sometimes form two, or three sides of a limit triangle.
Definition
A ray Aa is a limiting parallel to a ray Bb if they are coterminal or if they lie on distinct lines not equal to the line AB, they do not meet, and every ray in the interior of the angle BAa meets the ray Bb.[1]
References
- ^ Hartshorne, Robin (2000). Geometry: Euclid and beyond (Corr. 2nd print. ed.). New York, NY [u.a.]: Springer. ISBN 978-0387-98650-0.