Can you draw 2 parallel lines which can intersect. (Yes, it's possible)?

Answer 1

If you are talking about ordinary lines and ordinary geometry, then parallel lines do not meet. For example, the line x=1 and the line x=2 do not meet at any point, since the x coordinate of a point cannot be both 1 and 2 at the same time.

In this context, there is no such thing as "infinity" and parallel lines do not meet.

However, you can construct other forms of geometry, so-called non-Euclidean geometries. For example, you can take the usual points of the plane and attach to them an additional point called "infinity" and consider all lines to also include this additional point. In this context, there is a single "infinity" location where all lines meet. In a geometry like this, all lines intersect at infinity, in addition to any finite point where they might happen to meet.

Or, you could attach not just one additional point, but a whole collection of additional points, one for each direction. Then you can consider two parallel lines to meet at the extra point corresponding to their common direction, whereas two non-parellel lines do not intersect at infinity but intersect only at the usual finite intersection point. This is called projective geometry.

Answer 2

well, no, you can't. By definition, parallel lines do not intersect at any point. They always remain equal distance from each other. I suppose if you incorporated some sort of philosophetical statement, then maybe you could get away with it. But mathematically, no, they can not intersect.

Ok, you know, now that I think about this, I think you might be asking this the wrong way. Yes, if you draw the lines overlapping each other. but there's a difference between overlapping and intersecting. Intersecting means they cross over at a given point. Overlapping means they're on top of each other.

Answer 3

Yes, it is possible but not in plane geometry because in plane (Euclidean) geometry, one of the postulates which we assume is that parallel lines never intersect. So if I change this assumption, I can build a whole new geometry in which parallel lines do intersect.

Lo and behold, it is called spherical geometry. On a sphere, it is possible to draw two parallel lines which intersect. Just like how the longitude lines all connect at the poles. On a sphere (on the srface of the earth which is curved), it is also possible for me to draw a triangle with three 90 degrees angles which add up to more than 180 degrees.

Answer 4

In Euclidean geometry, this is impossible -- and it is even an axiom that they cannot intersect..

It is possible in some non-Euclidean geometries. It involves a different definition of what we mean by parallel. For example, on the surface of a sphere (like the Earth) straight lines that go north-south are actually great circles. Two lines that are parallel will intersect at exactly two points.

There are other gemoetries where parallel lines intersect as well.

Answer 5

No. Parallel lines never intersect - that's why they are parallel. If you are studying non-Euclidean geometry, lines which do not intersect are not parallel because the definition changes (i.e. a transversal that cuts one line at 90 degrees will not necessarily cut the other line at 90 degrees!! In fact it may not even intersect the other line!). As for lines of longitude and latitude on a globe - they are not an example of parallel lines! Gosh, mathematicians are stupid: these lines are curved lines (they are in fact not really straight lines - this stupidity started with the idiot Riemann). What does this mean? Well, when Euclid stated the postulates, he was referring to straight lines. So, in effect, parallel lines do not intersect in ANY geometry. This is another example of mathematician stupidity beyond belief!

Answer 6

I assume that's only possible if the two lines are parallel to other lines but not to each other. The point of being parallel is that they never intersect.

Answer 7

Do you mean the two lines intersect with eachother?

The very meaning of parallel is: "extending in the same direction, everywhere equidistant, and not meeting".

Either, you could draw to parallel lines on a paper, then bend the paper, but the lines would no longer be parallel. Or you could draw them on top of eachother, making them one line, and techincally not two parallel lines.

They can intersect with a third line, just not with eachother. Otherwise they are not parallel, according to the definition of "parallel".

Answer 8

Yes, but this is non-standard (Euclidean) geometry.
You can also draw triangles that are greater than 180 degrees. (drawing a triangle on a globe)
Let me find some links.
Check the link to find out.

The second link is what I am talking about.
To summarize, Hyperbolic lines can be parallel to one another, and yet still intersect, under Eulicid's definition of parallel lines.

Answer 9

NO.

In spherical geometry there are NO parallel lines. It is not that they intersect.

In Euclician geometry there is exactly 1 paralell line through a given point

In hyper (whatever its called) geometry there are infinite paralell lines through a given point.

However in the last case those points are not parallel to eachother they are parallel to the original line.

EDIT

Unless you allow intersections at infinity. Then there are parallel lines that intersect in hyperbolic geometry... but NO you can NOT 'Draw' them

Answer 10

On a plane, no, it's not possible. Parallel lines do not intersect in Euclidean geometry.

In spherical geometry, though, if you consider longitude lines to be "parallel" (they have the same angular degree measure between them), there are inifinitely many of them. (For example, 100°W and 120°W. They interesect at the north and south poles.)