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Definition of Parallel Lines 
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#1
Apr2304, 09:27 AM

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Can someone take a moment to give me the technical definition of a parallel line?



#2
Apr2304, 10:09 AM

P: 262

As far as i can remember in the Euclidian geometry
line A is parallel to line B if they don’t have any common point. Maybe there is another or even better definition to that. Moshek www.physicsforums.com/showthread.php?t=17243 


#3
Apr2304, 09:41 PM

PF Gold
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I would just add that in Euclidean (aka parabolic) geometry, given line B, there is exactly one line parallel to it. But there are other nonEuclidean geometries where there is no line parallel to line B, or at least two lines parallel to line B.
You may be interested in reading about Euclid's fifth postulate and all the doomed attempts to prove it just google Euclid's fifth postulate ;) Happy thoughts Rachel 


#4
Apr2304, 11:16 PM

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Definition of Parallel Lines
If I'm not completely daft, the definition of a parallel line is a line that lies in the same plane as another but they will never meet.



#5
Apr2404, 12:59 AM

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I think that is correct. Rachel 


#6
Apr2404, 01:51 AM

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#7
Apr2404, 04:10 AM

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Is that correct? I didn't think parallel lines had to lie in the same plane. I thought it was just that two lines are parallel if they never intersect, as Moshek said.
Rachel 


#8
Apr2404, 04:19 AM

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#9
Apr2404, 07:41 AM

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(at least in the text I've been looking at recently) two lines are said to be parallel if they don't intersect or are the same line.
This can be refined by saying two lines are skew parallel if they don't lie in the same plane, and antiparallel if you have directed lines and they point in opposite directions. 


#10
Apr2404, 08:10 AM

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It's different in this way? Ex.
Draw a circle and its origin. Imagine the origin is a point on a line extending toward and away from you, perpendicular to the screen/page. Every line tangent to the circle will never intersect the line through the origin, and by my definition is parallel. Now, extend the tangent lines to planes in the same way the origin was extended to a line, perpendicular to the page. Every line in these "tangent planes" is also parallel to the origin line. However, by adding the "in the same plane" requirement, in each tangent plane, only the lines perpendicular to the page would be parallel to the line through the origin.? Please check, I make mistakes effortlessly Rachel (Not to mention I already wrote this post and lost it! so am annoyed) 


#11
Apr2404, 09:09 AM

P: 262

Hurkyl Hi:
I like the idea that two line that are the same are parallel, it's nice and i did not know that. Thank you. Moshek 


#12
Apr2604, 06:23 AM

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Interesting. I would have sworn that every book I've looked in used "parallel" only to mean lines in the same plane that do not intersect and "skew" for lines that do not lie in one plane.



#13
Apr2704, 09:49 AM

P: 1,499

Dammit, I only wanted the orthodox textbook definition and already we're into nonEuclidean geometry and differences of opinion. That's what I love about this place. Thanks for all this.



#14
Apr2704, 11:07 AM

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#15
Apr2704, 11:16 AM

P: 262

Canute, That's is really Great ! And what do you know or think about nonEuclidian mathematics ? like of: http://www.gurdjieffinternet.com/bo...php?authID=121 Moshek 


#16
Apr2704, 04:27 PM

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I have seen the definitions go the other way as well. I think the convention adopted depends on if you're taking a synthetic approach or an analytical approach.



#17
Apr2804, 06:41 AM

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It's probably another of those blasted "physicists versus mathematicians" things!



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