# Are Circles parallel to straight lines

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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,

I'm just curious.

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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#2

"Lines in a plane" here is referring to straight lines

A circle is not a straight line

A circle is not a straight line

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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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(Original post by

"Lines in a plane" here is referring to straight lines

A circle is not a straight line

**13 1 20 8 42**)"Lines in a plane" here is referring to straight lines

A circle is not a straight line

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

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.

**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.

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(Original post by

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,

I'm just curious.

**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.

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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(Original post by

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.

**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.

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