Parallel Lines - I'm an idiot.

[Llama]

(Assume the top set of lines is a single line)

________________________
........................................__________ (Top line m)


__________________________________ (Bottom line l)

Are these parallel lines?

I know they are parallel in the sense they are going in the same direction, my question is whether the above can be called a parallel line since it's vertical distance from the bottom line has changed.

Wikipedia seems to tell me no
"Given straight lines l and m, the following descriptions of line m equivalently define it as parallel to line l in Euclidean space:
Every point on line m is located at exactly the same minimum distance from line l (equidistant lines)."

This isn't a maths homework question or anything, I'm just genuinely not sure what the answer is :S

 

[bam23]

they still aren't intersecting. at worst you have 3 parallel lines

 

[Llama]

But *can* I have 2?
I know I can have 3!

 

[DEATHMASTER]

Your confusion confuses me. They are parallel.

 

[Llama]

---
....---
........----
...-------------

They could meet, if I continued the same steps. In which case they wouldn't be parallel?
The distance between M and L changes!
If it because the top line can be a series of parallel lines, but not one single line?

 

[bam23]

they are parallel because they don't intersect. as long as them lines don't get in each other's grills then they're parallel. if they're breaking up like that into steps i dont think you consider them as one line anymore. so every 'step' until the step that hits the bottom line isn't parallel

 

[Acepilotf14]

As long as two lines never intersect, they are parallel.

If two lines intersect(even if they would only intersect a long long way off the paper/screen), they are perpendicular.

It's really easy.

 

[Llama]

Pretty sure that's cleared it up, thanks.

 

[mindless_moder]

As long as two lines never intersect, they are parallel.

If two lines intersect(even if they would only intersect a long long way off the paper/screen), they are perpendicular.

It's really easy.

perpendicular is not the opposite of parallel , also what you have stated isn't strictly true. It only applies to 2D space.

 

[15357]

I actually can't figure out what the confusion was about...

 

[Acepilotf14]

perpendicular is not the opposite of parallel , also what you have stated isn't strictly true. It only applies to 2D space.

We're talking about lines.

 

[Raziaar]

I actually can't figure out what the confusion was about...

He wasn't sure on the actual definition of parallel lines. That's all.

Basically Llama, two lines are parallel if they are equidistant all along the line, and thus never cross, even out to infinity. In a textbook, if they look equidistant at all points, they most likely are.

 

[Vegeta897]

as long as them lines don't get in each other's grills

I didn't come into this thread expecting to laugh hard but I did.

 

[ktimekiller]

the confusion confuses me

 

[Avoidist]

A line can't have a discontinuity. So you have 3 lines, and they're parallel. At best, you have 2 lines, one with discontinuities, and they're mostly parallel except for the small perpendicular segment connecting the two pieces.

 

[mindless_moder]

We're talking about lines.

you can have lines in 3d space :|.

 

[Dan]

A line can't have a discontinuity. So you have 3 lines, and they're parallel. At best, you have 2 lines, one with discontinuities, and they're mostly parallel except for the small perpendicular segment connecting the two pieces.

^this^
You drew 3 line segments, not 2 lines.

 

[Wanted Bob]

you can have lines in 3d space :|.

Technically no. A line has no depth to it, it can only exist in 2D space. If someone tried to create a line it would turn out to be a polygon, as no object in 3D space can have no depth.

EDIT: Nevermind, what I said only applies to real world objects. When dealing with vectors in 3D space, you are right.

 

[Stigmata]

Not quite. You have to separate "the abstract concept of a line" from objects that evoke lines, such as a length of string. The string forms a 1D line if held taut, while the string itself is still a 3D object.

[edit] Also, a line has no depth or width, only length, so by your logic it couldn't exist in 2D space either

 

[Wanted Bob]

Not quite. You have to separate "the abstract concept of a line" from objects that evoke lines, such as a length of string. The string forms a 1D line if held taut, while the string itself is still a 3D object.

[edit] Also, a line has no depth or width, only length, so by your logic it couldn't exist in 2D space either

Yes, right on both accounts. I admit my math skills are a little rusty...

 

[VirusType2]

Math? I can subtract money from my bank account. I'm somewhat of an expert.

 

[BabyHeadCrab]

Those aren't lines at all, they're highly imperfect line segments which would intersect p. quickly bro

 

[VirusType2]

 

[Llama]

OH, VIRUS, YOU SO FUNNY.
x

Someone was trying to tell me the first image I posted was 2 parallel lines, I thought it was 3. So it's cleared up.
(Most people won't get the confusion because I have a piss poor way of explaining what I'm trying to understand, sorry guys.)

 

[McGooTheWise]

We're talking about lines.

I thought perpendicular was when two lines intersect at a 90 degree angle...

 

[Acepilotf14]

I thought perpendicular was when two lines intersect at a 90 degree angle...

That's a right angle. All right angles are perpendicular, but not all perpendicular lines are right angles.

 

[PvtRyan]

That's a right angle. All right angles are perpendicular, but not all perpendicular lines are right angles.

http://www.google.com/search?q=define:perpendicular

 

[McGooTheWise]

Yeah, it's an angle, but it's not a right line. I say this because in my Math class we're doing the coordinate plane, and perpendicular is a right angled intersection. XP