Geometry of Continued Fractions

This book provides a new geometric approach to continued fractions, covering applications in Diophantine approximation, algebraic number theory, and toric geometry. It includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons, and new topics. The book offers an overview of current progress in the geometric theory of multidimensional continued fractions with illustrations and exercises.

Format: Hardback
Length: 451 pages
Publication date: 29 May 2022
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

This groundbreaking book presents a novel geometric perspective on continued fractions, unveiling a wide range of applications to diverse fields such as Diophantine approximation, algebraic number theory, and toric geometry. In its second edition, this comprehensive text delves into a geometric approach to Gauss Reduction Theory, classifies integer regular polygons, and introduces several fresh topics. While continued fractions have historically been a domain of number theory, their significance extends to dynamical systems, algebraic geometry, topology, and even celestial mechanics. The advent of computational geometry has sparked a renewed fascination with multidimensional generalizations of continued fractions, leading to the extension of numerous classical theorems to this realm. The reader will embark on a journey of exploration, gaining a comprehensive overview of the current state-of-the-art in the geometric theory of multidimensional continued fractions, while also being introduced to intriguing open problems. Throughout the book, illustrative figures and examples accompany the theoretical discussions, enhancing the understanding and visual appeal of the material. Each chapter includes a wealth of exercises designed to cater to undergraduate and graduate courses, fostering a deeper grasp of this intricate subject.

Weight: 842g
Dimension: 160 x 240 x 34 (mm)
ISBN-13: 9783662652763
Edition number: 2nd ed. 2022