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Geometry of Continued Fractions

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Cover of 'Geometry of Continued Fractions'

Table of Contents

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    Book Overview
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    Chapter 1 Classical Notions and Definitions
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    Chapter 2 On Integer Geometry
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    Chapter 3 Geometry of Regular Continued Fractions
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    Chapter 4 Complete Invariant of Integer Angles
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    Chapter 5 Integer Trigonometry for Integer Angles
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    Chapter 6 Integer Angles of Integer Triangles
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    Chapter 7 Continued Fractions and $\operatorname{SL}(2,{\mathbb{Z}})$ Conjugacy Classes. Elements of Gauss’s Reduction Theory. Markov Spectrum
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    Chapter 8 Lagrange’s Theorem
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    Chapter 9 Gauss–Kuzmin Statistics
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    Chapter 10 Geometric Aspects of Approximation
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    Chapter 11 Geometry of Continued Fractions with Real Elements and Kepler’s Second Law
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    Chapter 12 Extended Integer Angles and Their Summation
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    Chapter 13 Integer Angles of Polygons and Global Relations for Toric Singularities
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    Chapter 14 Basic Notions and Definitions of Multidimensional Integer Geometry
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    Chapter 15 On Empty Simplices, Pyramids, Parallelepipeds
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    Chapter 16 Multidimensional Continued Fractions in the Sense of Klein
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    Chapter 17 Dirichlet Groups and Lattice Reduction
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    Chapter 18 Periodicity of Klein Polyhedra. Generalization of Lagrange’s Theorem
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    Chapter 19 Multidimensional Gauss–Kuzmin Statistics
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    Chapter 20 On Construction of Multidimensional Continued Fractions
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    Chapter 21 Gauss Reduction in Higher Dimensions
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    Chapter 22 Approximation of Maximal Commutative Subgroups
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    Chapter 23 Other Generalizations of Continued Fractions
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Geometry of Continued Fractions
Published by
Springer Berlin Heidelberg, January 2013
DOI 10.1007/978-3-642-39368-6
978-3-64-239367-9, 978-3-64-239368-6

Oleg Karpenkov, Karpenkov, Oleg

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Mendeley readers

The data shown below were compiled from readership statistics for 12 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 12 100%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 5 42%
Other 2 17%
Student > Postgraduate 1 8%
Professor 1 8%
Student > Bachelor 1 8%
Other 4 33%
Readers by discipline Count As %
Mathematics 6 50%
Computer Science 3 25%
Unspecified 2 17%
Earth and Planetary Sciences 1 8%
Social Sciences 1 8%
Other 1 8%