ID - 131910119 TI - Geometry of Continued Fractions PY - 2022 SN - 9783662652770 9783662652763 9783662652787 9783662652794 PB - Berlin Springer DB - UniCat KW - Number theory KW - Ordered algebraic structures KW - Algebra KW - Geometry KW - Functional analysis KW - Numerical approximation theory KW - Discrete mathematics KW - Geology. Earth sciences KW - Computer science KW - algebra KW - discrete wiskunde KW - informatica KW - wiskunde KW - getallenleer KW - geofysica KW - geometrie KW - Algebra. KW - Fraccions contínues KW - Geometria de nombres UR - https://www.unicat.be/uniCat?func=search&query=sysid:131910119 AB - This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses. ER -