This talk reports on a mixture of old and new
work concerning the construction of representations of
the modular group into Isom(X) using Pappus's Theorem.
Here X = SL_3(R)/SO(3) . One new thing is the interpretation
of the Pappus modular groups as symmetry groups of patterns of geodesics
in X which have the same asymptotic properties as the edges
of the Farey triangulation of the hyperbolic plane. I will explain
at least briefly how this point of view leads to a complete
characterization of the Barbot component of discrete faithful
representations of the modular group into Isom(X).
