Re: [math-fun] Homotheties of the hyperbolic plane

On 2/14/08, Dan Asimov <dasimov@earthlink.net> wrote:

... In any case, the impossibility of a bijection H^2 -> H^2 that increases all distances by a factor of (say) 2 brings up an interesting question: Can one quantify just how close one can get to such a map?

In particular, can one choose constants c1, c2 both > 1 such that c1 <= |f(x) - f(y)| / |x - y| <= c2 ? WFL