On http://en.wikipedia.org/wiki/Hypercycle_%28geometry%29 I found the statement.
The hypercycles through a given point that share a tangent through that point converge towards a horocycle as their distances go towards infinity.
But I don't understand it.
hypercycles are curves (equidistant to some line)
- How do you get their tangent at a (given) point?
And what does the rest of the statement mean? can somebody give a proof and a picture?