Lectures on the Icosahedron and the solution of equations of the fifth degree:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Cosimo Classics
2007
|
| Edition: | [Nachdr. der 2. ed. 1913] |
| Series: | Cosimo classics : science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 289 S. |
| ISBN: | 9781602063068 |
Staff View
MARC
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| 240 | 1 | 0 | |a Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5. Grade |
| 245 | 1 | 0 | |a Lectures on the Icosahedron and the solution of equations of the fifth degree |
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Record in the Search Index
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|---|---|
| adam_text | TABLE
OF CONTENTS
PART I
THEORY OF THE ICOSAHEDRON ITSELF
CHAPTER I
The Regular Solids and the Theory of Groups.
8KQ.
·
PIS!
1.
Statement of the question
........ 3
2.
Preliminary notions of the group-theory
..... 6
3.
The cyclic rotation
groupa
........ -8
4.
The group of the dihedral rotations
...... 10
6.
The quadratic group
......... 13
β.
The group of the tetrahedral rotations
..... 14
7.
The group of the octahedral rotations
..... 16
8.
The group of the icosahedral rotations
..... 17
9.
On the planes of symmetry in our configurations
... 21
10.
General groups of points
—
Fundamental domains
... 23
11.
The extended groups
......... 24
12.
Generation of the icosahedral group
...... 26
13.
Generation of the other groups of rotations
.... 29
CHAPTER II
Introduction of (x + iy).
1.
First presentation and survey of the developments of this
chapter
...........31
2.
On those linear transformations of (z+iy) which correspond to
rotations round the centre
.......34
3.
Homogeneous linear substitutions
—
Their composition
. . 37
4.
Return to the groups of substitutions
—
The cyclic and dihedral
groupe
...........39
6.
The groups of the tetrahedron and octahedron
.... 40
xi
xii
TABLE
OF
CONTENTS
SIO.
6.
The icosahedral group
........ 43
7.
Non-homogeneous substitutions
—
Consideration of the ex¬
tended groups
......... 46
8.
Simple isomorphism in the case of homogeneous groups of
substitutions
........·■ 48
9.
Invariant forms belonging to a group
—
The set of forms for
the cyclic and dihedral groups
...... 50
10.
Preparation for the tetrahedral and octahedral forms
· · 54
11.
The set of forms for the tetrahedron
...... 55
12.
The set of forms for the octahedron
...... 58
13.
The set of forms for the icosahedron
...... 60
14.
The fundamental rational functions
...... 63
15.
Remarks on the extended groups
......
6β
CHAPTER III
Statement and Discussion of the Fundamental Pboblem,
according to the t.he0by of functions.
1.
Definition of the fundamental problem
..... 67
2.
Reduction of the
forna-problem
....... 69
3.
Plan of the following investigations
...... 72
4.
On the conformable representation by means of the function
ζ Ζ
74
5.
March
oí
the
г„
%%
function in general
—
Development in
аеііев
. 77
6.
Transition to the differential equations of the third order
. 79
7.
Connection with linear differential equations of the second
order
........... 81
8.
Actual establishment of the differential equation of the third
order for z[Z]
.......... 83
9.
Linear differential equations of the second order for zt and
üj
. 85
10.
Relations to Riemann s P-funetion
...... 87
CHAPTER IV
On the Algebraical Character of our
Fundamental
Problem.
1.
Problem of the present chapter
....... 90
2.
On the group of an algebraical equation
..... 91
3.
General remarks on resolvents
....... 94
4.
The Galoie resolvent in particular
...... 97
6.
Marshalling of our fundamental equations
.... 100
6.
Consideration of the form-problem«
...... 103
TABLE
OF
CONTENTS
xiii
SBC.
PAOS
7.
The solution of the equations of the
điheđron,
tetrahedron,
and octahedron
......... 104
8.
The resolvents of the fifth degree for the icosahedral equation
106
9.
The resolvent of the r a
........ 108
10.
Computation of the forms
t
and
W
......
Ill
11.
The resolvent of the tt s
........ 113
12.
The canonical resolvent of the J s
...... 114
13.
Connection of the new resolvent with the resolvent of the r s
. 116
14.
On the products of differences for the
« s
and the Y s
. . 117
15.
The simplest resolvent of the sixth degree
. . . .119
16.
Concluding remarks
......... 122
CHAPTEE V
General Theorems and Subvey of
гне
Subject.
1.
Estimation of our process of thought so far, and generalisations
thereof
...........124
2.
Determination of all finite groups of linear substitutions of a
variable
...........
Ї26
3.
Algebraically
integrable
linear homogeneous differential equa¬
tions of the second order
.......132
4.
Finite groups of linear substitutions for a greater number of
variables
.......... 135
5.
Preliminary glance at the theory of equations of the fifth
degree, and formulation of a general algebraical problem
. 137
6.
Infinite groups of linear substitutions of a variable
. . . 139
7.
Solution of the tetrahedral, octahedral, and icosahedral equa¬
tions by elliptic modular functions
.....144
8.
Formulée
for the direct solution of the simplest resolvent of
the sixth degree for the icosahedron
.....147
9.
Significance of the transcendental solutions
.... 148
|
| any_adam_object | 1 |
| author | Klein, Felix 1849-1925 |
| author_GND | (DE-588)11856286X |
| author_facet | Klein, Felix 1849-1925 |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV035236985 |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)634554740 (DE-599)BVBBV035236985 |
| discipline | Mathematik |
| edition | [Nachdr. der 2. ed. 1913] |
| era | Geschichte 1884 gnd |
| era_facet | Geschichte 1884 |
| format | Book |
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| isbn | 9781602063068 |
| language | English |
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| physical | XVI, 289 S. |
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| spelling | Klein, Felix 1849-1925 Verfasser (DE-588)11856286X aut Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5. Grade Lectures on the Icosahedron and the solution of equations of the fifth degree [Nachdr. der 2. ed. 1913] New York, NY Cosimo Classics 2007 XVI, 289 S. txt rdacontent n rdamedia nc rdacarrier Cosimo classics : science Geschichte 1884 gnd rswk-swf Polyeder (DE-588)4132101-7 gnd rswk-swf Gleichung (DE-588)4021246-4 gnd rswk-swf Grad 5 (DE-588)4366323-0 gnd rswk-swf Ikosaeder (DE-588)4161254-1 gnd rswk-swf (DE-588)4135952-5 Quelle gnd-content Ikosaeder (DE-588)4161254-1 s Gleichung (DE-588)4021246-4 s Grad 5 (DE-588)4366323-0 s Geschichte 1884 z DE-604 1\p DE-604 Polyeder (DE-588)4132101-7 s 2\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017042829&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Klein, Felix 1849-1925 Lectures on the Icosahedron and the solution of equations of the fifth degree Polyeder (DE-588)4132101-7 gnd Gleichung (DE-588)4021246-4 gnd Grad 5 (DE-588)4366323-0 gnd Ikosaeder (DE-588)4161254-1 gnd |
| subject_GND | (DE-588)4132101-7 (DE-588)4021246-4 (DE-588)4366323-0 (DE-588)4161254-1 (DE-588)4135952-5 |
| title | Lectures on the Icosahedron and the solution of equations of the fifth degree |
| title_alt | Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5. Grade |
| title_auth | Lectures on the Icosahedron and the solution of equations of the fifth degree |
| title_exact_search | Lectures on the Icosahedron and the solution of equations of the fifth degree |
| title_full | Lectures on the Icosahedron and the solution of equations of the fifth degree |
| title_fullStr | Lectures on the Icosahedron and the solution of equations of the fifth degree |
| title_full_unstemmed | Lectures on the Icosahedron and the solution of equations of the fifth degree |
| title_short | Lectures on the Icosahedron and the solution of equations of the fifth degree |
| title_sort | lectures on the icosahedron and the solution of equations of the fifth degree |
| topic | Polyeder (DE-588)4132101-7 gnd Gleichung (DE-588)4021246-4 gnd Grad 5 (DE-588)4366323-0 gnd Ikosaeder (DE-588)4161254-1 gnd |
| topic_facet | Polyeder Gleichung Grad 5 Ikosaeder Quelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017042829&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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