Karmaşık sürekli kesirler üzerine

We study simple continued fractions with entries from the ring of Gaussian integers, and more generally ring of integers of norm-Euclidean imaginary quadratic number fields (i.e. those number fields which admit a Euclidean norm). These number fields are necessarily of class number 1. The aim of this thesis is to demonstrate that from an algebraic and geometric viewpoint the theory of simple con tinued fractions with entries from integers is parallel to the that of simple continued fractions with entries from aforementioned rings. In order to demonstrate, we interpret the classical theory of simple continued fractions in terms of a one-dimensional cell complex (in fact, the familiar bipartite Farey tree) admitting an action of the modular group. This free action allows us to use elements of the modular group to label one-cells of the bipartite Farey tree. As a result, we may associate a finite (resp. infinite) path (a subcell-complex) based at the edge labeled I to any finite (resp. infinite) simple continued fraction.