I hope I am using the right terms here. But as I recall from math class (and bear with me, it’s been a while), asymptotic lines get closer and closer, but never really touch.

But is that true? Do they **really** never touch, or do they some day? Seems to depend on who you ask. My HS geometry teacher said No. But some people say they eventually do. Guess it depends on how you define infinity.

Also, I don’t mean to answer my own question (partly at least). But when I took Calculus, we sometimes used an integral to find the area under a curve. If it was asymtotic, the area eventually converged. If it wasn’t, no area could be found. I just thought I’d toss that out.

Also, a famous man once said, infinity is where parallel lines cross. Now, unlike asymptotic lines, parallel lines don’t bend into each other. So what on earth was he talking about? Does anyone know what quote I am talking about? If I had a cite, I’d include it. But really, was he just talking about asymptotic lines? I know some people say **ALL** space curves. So the shortest distance between two points is a curve. Is that what he meant?

Thank you in advace to all who reply:).