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

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,Die Statik des starren K?rpers,this important subject (the study of best approximations, badly approximable numbers, etc.). In this chapter we consider two geometric questions of approximations by continued fractions. First, we prove two classical results on best approximations of real numbers by rational numbers. Second, we desc

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,Einführung in die Kinematik und Kinetik,is not a natural question within the theory of continued fractions. One can hardly imagine any law to write the continued fraction for the sum directly. The main obstacle here is that the summation of rational numbers does not have a geometric explanation in terms of the integer lattice. In this cha

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,Gleichgewicht gestützter K?rper, integer invariants. Further, we use them to study the properties of multidimensional continued fractions. First, we introduce integer volumes of polytopes, integer distances, and integer angles. Then we express volumes of polytopes, integer distances, and integer angles in terms of integer volumes

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Oleg KarpenkovNew approach to the geometry of numbers, very visual and algorithmic.Numerous illustrations and examples.Problems for each chapter.Includes supplementary material:

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Springer-Verlag Berlin Heidelberg 2013