How to tell if two lines are parallel. Basically what I'm wondering is if just never touching qualifies the two lines as being parallel. Obviously this means the lines never approach each other when it comes to straight lines, but what about parabolas such as x^2 and x^2 + 1 which seem to be parallel as they never touch (only get infinitely close to each other.

Question

anonymous · Answer

The parabolas I was talking about

anonymous · Answer

Or is it Paraboli?

anonymous · Answer

when the slopes r equal and only then the 2 lines hv to be parallel

ganeshie8 · Answer

we can define them as parallel lines in a new geometry, there is absolutely no problem !

they just don't fit the `parallel line` definition of euclid :

`14.  Parallel lines are straight lines that are in the same plane and do not meet, no matter how far extended in either direction.`

as parabola is never straight

kainui · Answer

Well you're definitely right that they will never cross each other. At first my thought was to say that we could look at these as two slices from conic sections from two parallel planes.

This is definitely an interesting take on parallel lines, I have never thought of this before and I like it. Hyperbolic and spherical geometry are based on the parallel line definition of euclid being changed. Interesting idea to think about.

anonymous · Answer

oooohhh I kinda get that... nonamenever gives a good way to look at it also as the value of the derivative will be equal for both equations for every value of x

ikram002p · Answer

well pasicly two lines are parallel when they have no common points , according to hyperbolic geometry this is an example|dw:1406461806773:dw|