Can I transform the triangle in the right hand side to a triangle in the left hand side by a Mobius transform?
If $PSL(2, \mathbb{R})$ acts doubly transitive on $\mathbb{R} \cup \infty$, then do we transform right triangle to left triangle?
I know that $PSL(2, \mathbb{R})$ triple transitively on boundary of the upper half plane, which is $\Bbb R \cup \{ \infty \}$. But is it true that $PSL(2, \mathbb{R})$ acts doubly transitive on $\mathbb{R} \cup \infty$?