| 书目名称 | Geometry of Continued Fractions |
| 编辑 | Oleg N. Karpenkov |
| 视频video | |
| 概述 | New approach to the geometry of numbers, very visual and algorithmic.Numerous illustrations and examples.Problems for each chapter |
| 丛书名称 | Algorithms and Computation in Mathematics |
| 图书封面 |  |
| 描述 | .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.. |
| 出版日期 | Textbook 2022Latest edition |
| 关键词 | algebraic irrationalities; continued fractions; generalized continued fractions; integer trigonometry; u |
| 版次 | 2 |
| doi | https://doi.org/10.1007/978-3-662-65277-0 |
| isbn_softcover | 978-3-662-65279-4 |
| isbn_ebook | 978-3-662-65277-0Series ISSN 1431-1550 |
| issn_series | 1431-1550 |
| copyright | Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
发表于 2025-3-21 19:18:58
