Can two skew lines in parallel planes ever intersect?

[samoth]

It all depends on the geometry. If you're talking about a differentiable manifold or something, then the geometry is intrinsic and locally defined by a metric. Curvature and topology are some of the most weird and difficult areas in mathematics.

If you're assuming a well-behaved system with infinitely long planes in euclidean 2-space, then I believe it's true. (I think it might always be true if you reduce the system enough.)

The biggest thing in pure mathematics is defining the system. I would think it would be relatively straightforward to formulate a layman's "proof" in E2 using a few postulates from high school geometry. You could probably extend the proof to higher dimensions, too, since they're all orthogonal.

 

[puddlemonkey]

 

[*ebony*]

LOL...samoth if anyone can figure out a way i would bet on you!lol

i forgot about euclideans..... well the definition for parallel lines is different is it not when it's discussed with respect to non-euclidean gemotries. if i remember correctly it calls parallel lines those which, at some point, are both at right angles to a third line? the normal parallel lines have this property too. arn't the lines in non-euclidean geometries with this property are also called parallel, and these types of lines could be shown to meet in some situations.

In normal cases, we call parallel lines those that do not intersect, and they happen to be mutually at right angles to another line, in fact infinitely many lines........so they kind of took that aspect of parallel lines and made it part of a non-euclidean gemotrical definition for "parallel." dont ya think? this is just the impression I got anyways.

 

[nefertiti]

My head hurts.

 

[puddlemonkey]

My head hurts.

So many improper things to say I just can't settle on one

 

[*ebony*]

I don't beleive that, that is why i quit going to mine. Well not really, he died at like 45yo.
That was a great answere thou ebony, when I was reading I just kept thinking of your body as one plain and my body as the other.
Except my tangent kept crossing deep into your line....

OMG...lmao!!!!

 

[nefertiti]

So many improper things to say I just can't settle on one

lay 'em out there, I could use a smile lol.

 

[puddlemonkey]

lay 'em out there, I could use a smile lol.

I'll behave, sometimes I forget about the b/f and don't want to cross any lines. I'm working on being a better person, yay!

 

[chris302001]

I'll behave, sometimes I forget about the b/f and don't want to cross any lines. I'm working on being a better person, yay!

It's a trap!

 

[puddlemonkey]

It's a trap!