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Math Help - can curves be parallel to each other

  1. #1
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    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.
    Last edited by mg1912; April 6th 2009 at 09:54 PM.
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  2. #2
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    Quote Originally Posted by mg1912 View Post
    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.
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    Quote Originally Posted by Mush View Post
    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?
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  4. #4
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    Quote Originally Posted by mg1912 View Post
    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 ?

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  5. #5
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    Quote Originally Posted by Mush View Post
    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)
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  6. #6
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    Quote Originally Posted by ADARSH View Post
    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.
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  7. #7
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    Quote Originally Posted by masters View Post
    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?
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