# Are Circles parallel to straight lines

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#1
I was wondering if circles are parallel to straight lines if there are no points of intersection between the circle and the straight line.
This definition of being parallel (although from wikipedia) is:
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch at any point are said to be parallel
Is there any other conditions for something to be parallel?
I'm just curious.
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6 years ago
#2
"Lines in a plane" here is referring to straight lines
A circle is not a straight line
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6 years ago
#3
Depends in what type of geometry you are talking about. Look up euclidian geometry as well as positive and negative curvature. Lines that are parallel in the euclidian plane are straight, but those in negative curvature are curved, but still by definition parallel.
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#4
(Original post by 13 1 20 8 42)
"Lines in a plane" here is referring to straight lines
A circle is not a straight line
A plane is two dimensions, right?
A circle is in two dimensions and isn't a circle just a line?
Maybe I am just being stupid as the other poster wrote xD

(Original post by Protoxylic)
Depends in what type of geometry you are talking about. Look up euclidian geometry as well as positive and negative curvature. Lines that are parallel in the euclidian plane are straight, but those in negative curvature are curved, but still by definition parallel.
Ah, the reason I asked the questions is because I remember my Maths teacher telling me that it could be parallel but I didn't understand why at the time.
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6 years ago
#5
(Original post by Windowswind123)
I was wondering if circles are parallel to straight lines if there are no points of intersection between the circle and the straight line.
This definition of being parallel (although from wikipedia) is:
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch at any point are said to be parallel
Is there any other conditions for something to be parallel?
I'm just curious.
Two *lines* are parallel. A *line* is strictly a straight line, while a circle is an example of a curve. (Lines are also examples of curves.)

However, a line can lie tangent to a circle at a given point, or it can fail to intersect anywhere.

If you consider the point at infinity to be a genuine point, and the rest of the real plane to make up a sphere with the point at infinity (as in the Riemann sphere) then in fact lines are simply special kinds of circle: they are circles which go through the point at infinity. Then in your "circle parallel to straight lines" idea, what you're really talking about is two non-intersecting circles.
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#6
(Original post by Smaug123)
If you consider the point at infinity to be a genuine point, and the rest of the real plane to make up a sphere with the point at infinity (as in the Riemann sphere) then in fact lines are simply special kinds of circle: they are circles which go through the point at infinity.
Thanks, I found that an interesting concept to read - I'll probably read up more about the point of infinity.
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