語系:
繁體中文
English
說明(常見問題)
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Geometry of Continued Fractions
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Geometry of Continued Fractions/ by Oleg N. Karpenkov.
作者:
Karpenkov, Oleg N.
面頁冊數:
XX, 451 p. 69 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Algebra. -
電子資源:
https://doi.org/10.1007/978-3-662-65277-0
ISBN:
9783662652770
Geometry of Continued Fractions
Karpenkov, Oleg N.
Geometry of Continued Fractions
[electronic resource] /by Oleg N. Karpenkov. - 2nd ed. 2022. - XX, 451 p. 69 illus.online resource. - Algorithms and Computation in Mathematics ;26. - Algorithms and Computation in Mathematics ;26.
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. Quadratic forms and Makov spectrum. -- Chapter 8. Geometric continued fractions -- Chapter 9. Continuant representation of GL(2,Z) Matrices -- Chapter 10. Semigroup of Reduced Matrices -- Chapter 11. Elements of Gauss reduction theory -- Chapter 12. Lagrange’s theorem -- Gauss-Kuzmin statistics -- Chapter 14. Geometric aspects of approximation -- Chapter 15. Geometry of continued fractions with real elements and Kepler’s second law -- Chapter 16. Extended integer angles and their summation -- Chapter 17. Integer angles of polygons and global relations for toric singularities -- Part II. Multidimensional continued fractions -- Chapter 18. Basic notations and definitions of multidimensional integer geometry -- Chapter 19. On empty simplices, pyramids, parallelepipeds -- Chapter 20. Multidimensional continued fractions in the sense of Klein -- Chapter 21. Dirichlet groups and lattice reduction -- Chapter 22. Periodicity of Klein polyhedral. Generalization of Lagrange’s Theorem -- Chapter 23. Multidimensional Gauss-Kuzmin Statistics -- Chapter 24. On the construction of multidimensional continued fractions -- Chapter 25. Gauss reduction in higher dimensions. Chapter 26. Approximation of maximal commutative subgroups -- Capter 27. Other generalizations of continued fractions. References. Index.
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.
ISBN: 9783662652770
Standard No.: 10.1007/978-3-662-65277-0doiSubjects--Topical Terms:
579870
Algebra.
LC Class. No.: QA150-272
Dewey Class. No.: 512
Geometry of Continued Fractions
LDR
:04136nam a22004095i 4500
001
1086775
003
DE-He213
005
20220528060119.0
007
cr nn 008mamaa
008
221228s2022 gw | s |||| 0|eng d
020
$a
9783662652770
$9
978-3-662-65277-0
024
7
$a
10.1007/978-3-662-65277-0
$2
doi
035
$a
978-3-662-65277-0
050
4
$a
QA150-272
072
7
$a
PBF
$2
bicssc
072
7
$a
MAT002000
$2
bisacsh
072
7
$a
PBF
$2
thema
082
0 4
$a
512
$2
23
100
1
$a
Karpenkov, Oleg N.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1393615
245
1 0
$a
Geometry of Continued Fractions
$h
[electronic resource] /
$c
by Oleg N. Karpenkov.
250
$a
2nd ed. 2022.
264
1
$a
Berlin, Heidelberg :
$b
Springer Berlin Heidelberg :
$b
Imprint: Springer,
$c
2022.
300
$a
XX, 451 p. 69 illus.
$b
online resource.
336
$a
text
$b
txt
$2
rdacontent
337
$a
computer
$b
c
$2
rdamedia
338
$a
online resource
$b
cr
$2
rdacarrier
347
$a
text file
$b
PDF
$2
rda
490
1
$a
Algorithms and Computation in Mathematics ;
$v
26
505
0
$a
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. Quadratic forms and Makov spectrum. -- Chapter 8. Geometric continued fractions -- Chapter 9. Continuant representation of GL(2,Z) Matrices -- Chapter 10. Semigroup of Reduced Matrices -- Chapter 11. Elements of Gauss reduction theory -- Chapter 12. Lagrange’s theorem -- Gauss-Kuzmin statistics -- Chapter 14. Geometric aspects of approximation -- Chapter 15. Geometry of continued fractions with real elements and Kepler’s second law -- Chapter 16. Extended integer angles and their summation -- Chapter 17. Integer angles of polygons and global relations for toric singularities -- Part II. Multidimensional continued fractions -- Chapter 18. Basic notations and definitions of multidimensional integer geometry -- Chapter 19. On empty simplices, pyramids, parallelepipeds -- Chapter 20. Multidimensional continued fractions in the sense of Klein -- Chapter 21. Dirichlet groups and lattice reduction -- Chapter 22. Periodicity of Klein polyhedral. Generalization of Lagrange’s Theorem -- Chapter 23. Multidimensional Gauss-Kuzmin Statistics -- Chapter 24. On the construction of multidimensional continued fractions -- Chapter 25. Gauss reduction in higher dimensions. Chapter 26. Approximation of maximal commutative subgroups -- Capter 27. Other generalizations of continued fractions. References. Index.
520
$a
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.
650
0
$a
Algebra.
$2
gtt
$3
579870
650
0
$a
Approximation theory.
$3
527707
650
0
$a
Convex geometry .
$3
1255327
650
0
$a
Discrete geometry.
$3
672137
650
0
$a
Number theory.
$3
527883
650
2 4
$a
Order, Lattices, Ordered Algebraic Structures.
$3
670104
650
2 4
$a
Approximations and Expansions.
$3
672153
650
2 4
$a
Convex and Discrete Geometry.
$3
672138
650
2 4
$a
Number Theory.
$3
672023
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783662652763
776
0 8
$i
Printed edition:
$z
9783662652787
776
0 8
$i
Printed edition:
$z
9783662652794
830
0
$a
Algorithms and Computation in Mathematics ;
$v
26
$3
1393616
856
4 0
$u
https://doi.org/10.1007/978-3-662-65277-0
912
$a
ZDB-2-SMA
912
$a
ZDB-2-SXMS
950
$a
Mathematics and Statistics (SpringerNature-11649)
950
$a
Mathematics and Statistics (R0) (SpringerNature-43713)
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼[密碼必須為2種組合(英文和數字)及長度為10碼以上]
登入