# Thread: can curves be parallel to each other

1. ## can curves be parallel to each other

they can. when we are talking about parallel, it can be concluded into 2 situations, the parallel of straight lines and the parallel of curves. the situation of straight lines is just a particular example of paralle.
there are many example of parallel of curves, for example, concentric circles, tortuous railway and so on. the essential character of parallel is a certain unchange distance, the concentric circles is a good example of this. at the same time circles are also curves. so curves can be parallel to each other.

2. Originally Posted by mg1912
they can. when we are talking about parallel, it can be concluded into 2 situations, the parallel of straight lines and the parallel of curves. the situation of straight lines is just a particular example of paralle.
there are many example of parallel of curves, for example, concentric circles, tortuous railway and so on. the essential character of parallel is a certain unchange distance, the concentric circles is a good example of this. at the same time circles are also curves. so curves can be parallel to each other.
I wouldn't say that the circles themselves are parallel, but I be more inclined to state that the tangents at corresponding points are parallel, which reduces it to a straight line situation.

3. Originally Posted by Mush
I wouldn't say that the circles themselves are parallel, but I be more inclined to state that the tangents at corresponding points are parallel, which reduces it to a straight line situation.
I think any two points always are parallel.because they is always the same distance apart.
circle is made up of infinite points,so Corresponding points of circles are always the same distance apart,then concentric circles are parallel.
I'm sorry,My native language is Chinese,Do I make myself clear?

4. Originally Posted by mg1912
I think any two points always are parallel.because they is always the same distance apart.
circle is made up of infinite points,so Corresponding points of circles are always the same distance apart,then concentric circles are parallel.
I'm sorry,My native language is Chinese,Do I make myself clear?
points are parallel !?!

can you tell me which points are you talking, how will you explain the points you have selected ?

even in-case of straight lines have you heard parallel rectangle ?

5. Originally Posted by Mush
I wouldn't say that the circles themselves are parallel, but I be more inclined to state that the tangents at corresponding points are parallel, which reduces it to a straight line situation.
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a ...
en.wikipedia.org/wiki/Parallel_(geometry)

A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel lines.
en.wikipedia.org/wiki/Parallel_(curve)

points are parallel !?!

can you tell me which points are you talking, how will you explain the points you have selected ?

even in-case of straight lines have you heard parallel rectangle ?
two fixed points are always the same distance apart.

7. Originally Posted by masters
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a ...
en.wikipedia.org/wiki/Parallel_(geometry)

A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel lines.
en.wikipedia.org/wiki/Parallel_(curve)
Do you think parallel?