INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783642393686
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52311
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Geometry of Continued Fraction
General Material Designation
[Book]
Other Title Information
:[delta
First Statement of Responsibility
/ by Oleg Karpenkov
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Berlin, Heidelberg
Name of Publisher, Distributor, etc.
: Springer Berlin Heidelberg :Imprint: Springer,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XVII, 405 p. 114 illus., online resource.
SERIES
Series Title
(Algorithms and Computation in Mathematics,1431-1550
Volume Designation
; 26)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
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 tosuch areas asDiophantine 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.
Text of Note
Preface -- Introduction -- Part 1. Regular continued fractions: Chapter 1. Classical notions and definitions -- Chapter 2. On integer geometry -- Chapter 3. Geometry of regular continued fractions -- Chapter 4. Complete invariant of integer angles -- Chapter 5. Integer trigonometry for integer angles -- Chapter 6. Integer angles of integer triangles -- Chapter 7. Continued fractions and SL(2; Z) conjugacy classes. Elements of Gauss Reduction Theory. Markoff spectrum -- Chapter 8. Lagrange theorem -- Chapter 9. Gauss-Kuzmin statistics -- Chapter 10. Geometric approximation aspects -- Chapter 11. Geometry of continued fractions with real elements and the second Kepler law -- Chapter 12. Integer angles of polygons and global relations to toric singularities -- Part 2. Klein polyhedra: Chapter 13. Basic notions and definitions of multidimensional integer geometry -- Chapter 14. On empty simplices, pyramids, parallelepipeds -- Chapter 15. Multidimensional continued fractions in the sense of Klein -- Chapter 16. Dirichlet groups and lattice reduction -- Chapter 17. Periodicity of Klein polyhedra. Generalization of Lagrange theorem -- Chapter 18. Multidimensional Gauss-Kuzmin statistics -- Chapter 19. On construction of multidimensional continued fractions -- Chapter 20. Gauss Reduction in higher dimensions -- Chapter 21. Decomposable forms. Relation to Littlewood and Oppenheim conjectures -- Chapter 22. Approximation of maximal commutative subgroups -- Chapter 23. Other generalizations of continued fractions -- Bibliography .?╗╣
SERIES
Title
Algorithms and Computation in Mathematics,1431-1550
Volume Number
26
TOPICAL NAME USED AS SUBJECT
Mathematics
Algebra
Discrete groups
Number theory
Electronic books
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Karpenkov, Oleg.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9783642393679.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9783642393679.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
