The question is as follows (by the way I'm asking here, cause the calculus and beyond forum seems to be primarily concerned with Calculus,DE, LA and AA):(adsbygoogle = window.adsbygoogle || []).push({});

let f(z)=(2z+1)/(z+1) be an isometry of the hyperbolic plane H={z| Im(z)>0}.

let l be a hyperbolic line in H which is invariatn under f, calculate the hyperbolic distance:

p(z,f(z)) for some z in l.

Now I want to use here the definition of the hyperbolic distance given by the cross ratio.

So I found the fixed points of f, which are: w=(1+-(sqrt(5))/2, those points are in l (or so I think), from here we can use the cross ration definition, i.e:

p(z,f(z))=[tex]log(D(w_1,z,f(z),w_2)[/tex] where D is the double cross ration defined by:

D(z1,z2,z3,z4)=(z1-z3)(z2-z4)/((z1-z4)(z2-z3))

from here just plug and go, but is my appraoch correct?

thanks in advance.

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# Hyperbolic Distance and double Cross Ratio.

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