Algorithm of the generalizationued continued fraction

In Introduction we discuss the history of the continued fraction and of its generalizations. In § 1 we compare the geometric interpretations of the continued fraction given by Klein, by Voronoi and by author, and define the convex continued fraction. In § 2 we propose an algorithm of computation of the convex continued fraction. In § 3 we compare the geometric interpretations of the multidimensional generalizations of the continued fraction given by Klein, by Voronoi and by author (see preprint no. 86/2003). In § 4 we improve an algorithm of computation of a generalization of the covex continued fraction given by the author (preprint no. 10/2004). In § 5 we improve an algorithm for ordering three points on a plane.