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Titlebook: Geometry of Continued Fractions; Oleg Karpenkov Textbook 20131st edition Springer-Verlag Berlin Heidelberg 2013 algebraic irrationalities.

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發(fā)表于 2025-3-21 18:44:29 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Geometry of Continued Fractions
編輯Oleg Karpenkov
視頻videohttp://file.papertrans.cn/384/383801/383801.mp4
概述New approach to the geometry of numbers, very visual and algorithmic.Numerous illustrations and examples.Problems for each chapter.Includes supplementary material:
叢書名稱Algorithms and Computation in Mathematics
圖書封面Titlebook: Geometry of Continued Fractions;  Oleg Karpenkov Textbook 20131st edition Springer-Verlag Berlin Heidelberg 2013 algebraic irrationalities.
描述.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. 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 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 20131st edition
關(guān)鍵詞algebraic irrationalities; continued fractions; generalized continued fractions; integer trigonometry; u
版次1
doihttps://doi.org/10.1007/978-3-642-39368-6
isbn_ebook978-3-642-39368-6Series ISSN 1431-1550
issn_series 1431-1550
copyrightSpringer-Verlag Berlin Heidelberg 2013
The information of publication is updating

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發(fā)表于 2025-3-21 21:29:26 | 只看該作者
,L?sung der Fundamentalaufgaben,or infinite regular continued fractions. Further, we prove existence and uniqueness of continued fractions for a given number (odd and even continued fractions in the rational case). Finally, we discuss approximation properties of continued fractions.
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Grundgleichungen der Hydraulik,and unit determinant. We say that the matrices . and . from . are integer conjugate if there exists an . matrix . such that .=... A description of integer conjugacy classes in the two-dimensional case is the subject of Gauss’s reduction theory, where conjugacy classes are classified by periods of ce
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Einführung in die Technische Mechanike Lagrange’s theorem stating that every quadratic irrationality has a periodic continued fraction, conversely that every periodic continued fraction is a quadratic irrationality. One of the ingredients to the proof of Lagrange theorem is the classical theorem on integer solutions of Pell’s equation
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