ok, i know that this has in someway been answered before, and i am new here, i also am by far not a geometry major, but that is why i am asking here, because you peopl eknow this stuff. so here is the question the standard definition of parallel lines are two lines on the same plane that are of an equal distance (hence they will never intersect) i know there are non-standard or different definitions but i am trying to stay relativly basic here. i remember reading or hearing somewhere that if space had a positive or negative curvature to it that two parallel lines may actual seperate or intersect. so i have to ask if there is anyone that might be able to explain this, and alsoif they intersect how are they parallel, a part of me thinks that as soon as the distance between them increases or decrease or they intersect, they are not parallel lines so its ok if they intersect. sorry i know i am getting a bit on a tangent, i would appreciate any insight, or links so i could learn a bit more, or understand this a bit more.