Farey Boat: Continued Fractions and Triangulations, Modular Group and Polygon Dissections
We reformulate several known results about continued fractions in combinatorial terms. Among them the theorem of Conway and Coxeter and that of Series, both relating continued fractions and triangulations. More general polygon dissections appear when extending these theorems for elements of the modular group PSL(2,Z)\mathrm{PSL}(2,\mathbb {Z} These polygon dissections are interpreted as walks in the Farey tessellation. The combinatorial model of continued fractions can be further developed to obtain a canonical presentation of elements of PSL(2,Z)\mathrm{PSL}(2,\mathbb {Z}
Jahresbericht der Deutschen Mathematiker Vereinigung