# Ptolemy metric space. Help

1. Mar 7, 2009

### ypatia

Ptolemy metric space. Help!!

The problem is :
"Let x,y,z,t belongs to R^n where d(x,y)=||x-y||.
Show that(Ptolemy's inequality):
d(x,y)d(z,t)<=d(x,z)d(y,t)+d(x,t)d(y,z)"

I have found this related to the topic paper but I cannot show that the Euclidean space R^n is Ptolemy.
The paper in the second page "2.Preliminaries" says that "To show that the Euclidean space R^n is Ptolemy, consider again four points x,y,z,w. Applying a suitable Mobius transformation we can assume that z is a midpoint of y and w, i.e. |yz|=|zw|=1/2 |yw|. For this configuration...."
But how can we extract from the above paragraph that the Euclidean space R^n is Ptolemy and which is the "suitable Mobius transformation"??