Geometry of Continued Fractions

“Throughout the book many theorems are accompanied by constructive algorithms. Due to its rich content and connections to several parts of mathematics this volume will be of interest to graduate students and researchers not only in number theory and discrete geometry.” (C. Baxa, Monatshefte für Mathematik, Vo. 180, 2016)

“Karpenkov … begins with a distinctive treatment of continued fraction foundations emphasizing lattice geometry. One-dimensional continued fractions connect to two-dimensional lattices--very apt for illustration. … Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (10), June, 2014)

“The book is well written and is easy to read and navigate. … The book features a number of helpful illustrations and tables, a detailed index, and a large bibliography.This text is likely to become a valuable resource for researchers and students interested in discrete geometry and Diophantine approximations, as well as their rich interplay and many connections.” (Lenny Fukshansky, zbMATH, Vol. 1297, 2014)