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### Parallel Lines, Concentric Circles

```Date: 04/24/2003 at 21:29:03
From: Christina
Subject: Parallel lines

If parallel means that two lines never intersect, would the lines
that form a circle drawn inside another circle be considered parallel?
```

```
Date: 04/24/2003 at 23:38:48
From: Doctor Peterson
Subject: Re: Parallel lines

Hi, Christina.

Circles are not lines, so they can't be parallel lines. Remember, in
math a line is always a straight line.

We do sometimes talk about parallel curves, and when we do, concentric
circles (not just any circles one inside the other, but circles with
the same center) would be called parallel. In that case, though, the
definition is not that they are parallel if they don't intersect, but
that they are parallel because they are always the same distance
apart.

In fact, parallel lines are not really defined as any lines that don't
intersect. That is only true in a plane. Lines in different planes
(such as one edge of your ceiling, and a different edge of your floor)
don't intersect, but are not parallel. Parallel lines go in the same
direction, and remain the same distance apart everywhere.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 04/25/2003 at 11:02:48
From: Christina
Subject: Thank you (parallel lines)

Thank you for your quick reply!  I also appreciate that it is in
language that I can easily relay to my students.
```
Associated Topics:
High School Definitions
High School Euclidean/Plane Geometry
High School Higher-Dimensional Geometry

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