# Is there any term for 2 straight-lines not touching yet not equidistant?

In basic school mathematics, I was taught that a pair of straight lines could be either parallel (maintain the same distance between each other ie. Not cross, or intersecting (crossing) each other.

But it is very easy to find a third situation, where the 2 straight-lines are NOT maintaining equal-distance throughout their length, yet they are not crossing each other. Such as this:----

This condition could be easily imagined- if in my room I imagine a diagonal along the floor floor from South-East Corner (C) to North-west corner (D); and imagine another line, a diagonal along the ceiling from North-East-Corner (B) to South West Corner. The 2 straight lines obtained would never touch in a real and finite world, yet they are not parallel.

This is only one condition; many other similar conditions exist. Such as this one on a hexagonal prism (such as pencil)

What should I call them? Should I call them parallel? (since they will not cut anywhere)

• In 2 dimensional space, 2 lines are either crossing or parallel. In 3 dimensional space, 2 planes are either crossing or parallel. Lines in 3 dimensional space can be "neither". – David Jan 10 '17 at 20:11
• ^ And to build on Dave's answer, in 3-d space, if they are not parallel yet do not cross, they are called skew. – The Count Jan 10 '17 at 20:11
• The more dimensions the spaces gives you, the more possibilites to miss each other. 2D planes won't necessarly intersect in four dimensions. – Laray Jan 10 '17 at 20:12
• see this:mathworld.wolfram.com/SkewLines.html – Arnaldo Jan 10 '17 at 20:12
• You may write it as answer @TheCount – Always Confused Jan 10 '17 at 20:12

This logic applies to any dimension, an object in $n$ dimension is either parallel or intersecting if the dimension we are measuring in $=n+1$, but not if the dimension $\lt n+1$ In your example lines are $1$ dimensional, and you are calculating in the third dimension. because $1+1\lt3$, lines can be skew.