Different worlds, different tastes,
Different marks upon our face.
Parallel lines they sometime say,
Those two darn ideas, two separate ways.
They never touch, only extend,
On and on, they never bend.
So tell me how we redefine,
Circumvent the concept of parallel lines.
Now there’s a flaw with people’s thoughts,
They rarely think out side the box.
For human beings, although geometric designs,
Have a multitude of factors, unlike theories in time.
Though each one different, we’re all the same,
We’re parallel lines on different planes.
So there are instances it happens such,
That parallel lines they sometimes touch.
Note :
While in Euclidean geometry two geodesics can either intersect or be parallel, in general and in hyperbolic space in particular there are three possibilities. Two geodesics can be either:
- intersecting: they intersect in a common point in the plane
- parallel: they do not intersect in the plane, but do in the limit to infinity
- ultra parallel: they do not even intersect in the limit to infinity
In the literature ultra parallel geodesics are often called parallel. Geodesics intersecting at infinity are then called limit geodesics.
