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Titlebook: Geometry of Continued Fractions; Oleg N. Karpenkov Textbook 2022Latest edition Springer-Verlag GmbH Germany, part of Springer Nature 2022

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書目名稱Geometry of Continued Fractions
編輯Oleg N. Karpenkov
視頻videohttp://file.papertrans.cn/384/383800/383800.mp4
概述New approach to the geometry of numbers, very visual and algorithmic.Numerous illustrations and examples.Problems for each chapter
叢書名稱Algorithms and Computation in Mathematics
圖書封面Titlebook: Geometry of Continued Fractions;  Oleg N. Karpenkov Textbook 2022Latest edition Springer-Verlag GmbH Germany, part of Springer Nature 2022
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
關(guān)鍵詞algebraic irrationalities; continued fractions; generalized continued fractions; integer trigonometry; u
版次2
doihttps://doi.org/10.1007/978-3-662-65277-0
isbn_softcover978-3-662-65279-4
isbn_ebook978-3-662-65277-0Series ISSN 1431-1550
issn_series 1431-1550
copyrightSpringer-Verlag GmbH Germany, part of Springer Nature 2022
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Zeitstetige Zinsstrukturmodelle,heory. F. Klein generalized the notion of sail to the multidimensional case to study integer solutions of homogenous decomposable forms. We will study this generalization in the second part of this book.
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On Integer Geometrytions being associated to certain invariants of integer angles. The geometric viewpoint on continued fractions also gives key ideas for generalizing Gauss—Kuzmin statistics to studying multidimensional Gauss’s reduction theory, leading to several results in toric geometry.
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Classical Notions and Definitionsor 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. For more details on the classical theory of cont
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On Integer Geometry solution. In the next chapters we give an interpretation of the elements of continued fractions in terms of integer geometry, with the continued fractions being associated to certain invariants of integer angles. The geometric viewpoint on continued fractions also gives key ideas for generalizing G
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