[math-fun] Homotheties of the hyperbolic plane

I don't think I ever considered this before, but it seems I just figured out all possible ways such that, given a real number c > 0, one can construct a bijection of the hyperbolic plane H^2 to itself that multiplies all distances by c: f: H^2 -> H^2 such that dist(f(x),f(y)) = c dist(x,y) for all x, y in H^2. (If the word isn't "homothety", then I withdraw it.) I wonder if anyone else would care to tackle the same question. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele