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mg1912

Member

Registered: 2009-04-05

Posts: 5

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 (2009-04-05 18:44:32)

mg1912

Member

Registered: 2009-04-05

Posts: 5

Re: can curves be parallel to each other？

My native language is Chinese.so I do not write well.Do I make myself clear?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: can curves be parallel to each other？

Yes, quite clear!

I write about this here: Perpendicular and Parallel

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mg1912

Member

Registered: 2009-04-05

Posts: 5

Re: can curves be parallel to each other？

Yes, quite clear!

I write about this here: Perpendicular and Parallel

"Always the same distance apart and never touching"？
above,First picture's curves are intersectant,but they are parallel!

mg1912

Member

Registered: 2009-04-05

Posts: 5

Re: can curves be parallel to each other？

So parallel is always the same distance apart ,but do not no-touch.
Corresponding points are always the same distance apart.

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: can curves be parallel to each other？

Depends how you think about it, if you define a circular object as either a shape whose sides are negligible, or with ∞ tangents. You can state that two tangent lines are parallel, but that is because we only assume that there is a point on the circumference such that a straight line is existent. But if we think about a circle as having ∞ sides, then you *could* say that there is a point, ∞/2, which lies between two of the infinitesimal sides, but if we define this as a limit then we say that this is going to approach infinity. So what are we really saying when we say a circle can have ∞ tangents?

The concept is an interesting one, but as for the topic, you could say that a circle has either no parallel lines or ∞ parallel lines. Some people say that a circle has an infinite number of sides is just another proof that 0 ∙ (±∞) is an indetermination and not only 0.

mg1912

Member

Registered: 2009-04-05

Posts: 5

Re: can curves be parallel to each other？

Depends how you think about it, if you define a circular object as either a shape whose sides are negligible, or with ∞ tangents. You can state that two tangent lines are parallel, but that is because we only assume that there is a point on the circumference such that a straight line is existent. But if we think about a circle as having ∞ sides, then you *could* say that there is a point, ∞/2, which lies between two of the infinitesimal sides, but if we define this as a limit then we say that this is going to approach infinity. So what are we really saying when we say a circle can have ∞ tangents?

The concept is an interesting one, but as for the topic, you could say that a circle has either no parallel lines or ∞ parallel lines. Some people say that a circle has an infinite number of sides is just another proof that 0 ∙ (±∞) is an indetermination and not only 0.

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 circle with circle are parallel.

I'm sorry,My native language is Chinese,Do I make myself clear?