Descendants of the Mother of All Continued Fractions

Explore a mathematical lecture on the descendants of the "mother of all continued fractions" presented at the Erwin Schrödinger International Institute's Workshop on "Uniform Distribution of Sequences." Delve into Seidel's 1855 arithmetic procedure of contraction for generalized continued fractions (GCF) and Shunji Ito's 1989 planar natural extension of the Farey tent map. Learn how induced transformations of Ito's natural extension govern contractions of Farey expansions, giving birth to various GCF-algorithms including regular continued fractions, Kraaikamp's S-expansions, and Nakada's α-continued fractions. Discover new superoptimal continued fractions with simultaneous fast convergence and excellent approximation properties, developed through joint work with Karma Dajani and Cor Kraaikamp.