Definition:Parallel (Geometry)

As Euclid defined it:

"Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in either direction, do not meet one another in either direction."

Comment
Different geometries allow different conditions for the existence of parallel lines.


 * Euclidean geometry allows that exactly one line through a given point can be constructed parallel to a given line;
 * Hyperbolic geometry allows for an infinite number of such;
 * Elliptical geometry allows that no such lines can be constructed.