[math-fun] Continued fractions and the hyperbolic plane

It's well known that continued fractions and the (3,infty) tiling of the hyperbolic plane are deeply connected. What happens if we move to the (4,infty) tiling of the plane? It's the Cayley graph of the free group on two generators; as a gasket, you place two "equal" (in the hyperbolic sense) circles in the triangular gap instead of one. Do we get a notion of continued fraction with binary strings instead of natural numbers? What's analogous to the modular group? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com