Do Parallel Lines Intersect?

Date: 3/1/96 at 13:54:45
From: Ruthven-Ayrshire Student
Subject: Parallel Lines

I am a junior high mathematics teacher, and one of my classes is 
studying parallel lines.  I have heard once that parallel lines do in 
fact intersect.  I have brought the subject up in class and the students 
wanted to find any information about it.  If you can help us in any 
way, please respond.

Date: 3/1/96 at 14:15:38
From: Doctor Ethan
Subject: Re: Parallel Lines

Hello,

Well, I am afraid that parallel lines do not intersect.  In fact, that 
is the definition of parallel lines in a plane.  

I can think of two things that might be confusing this issue. The 
first has to do with perspective drawing.  In perspective drawing 
(imagine standing on straight railroad tracks that are going off into 
the distance), parallel lines appear to intersect.  

The other thing that you may be thinking about is that in some 
non-Euclidean geometry, parallel lines are not the same distance 
apart the whole time. However, I would not mention this to your 
students until you have time to read a little about hyperbolic 
geometry.

-Doctor Ethan,  The Math Forum