Introduction to the geometry of complex numbers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English French |
| Veröffentlicht: |
Mineola, NY
Dover Publications
2008
|
| Ausgabe: | Dover ed., 1. publ. |
| Schriftenreihe: | Dover books on mathematics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | Nachdr. der Ausg. Ungar, New York, 1956 |
| Beschreibung: | 208 S. graph. Darst. 22 cm |
| ISBN: | 9780486466293 0486466299 |
Internformat
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| 240 | 1 | 0 | |a Introduction à la géométrie des nombres complexes |
| 245 | 1 | 0 | |a Introduction to the geometry of complex numbers |c Roland Deaux. Transl. by Howard Eves |
| 250 | |a Dover ed., 1. publ. | ||
| 264 | 1 | |a Mineola, NY |b Dover Publications |c 2008 | |
| 300 | |a 208 S. |b graph. Darst. |c 22 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Dover books on mathematics | |
| 500 | |a Nachdr. der Ausg. Ungar, New York, 1956 | ||
| 650 | 4 | |a Numbers, Complex | |
| 650 | 4 | |a Geometry, Projective | |
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Datensatz im Suchindex
| _version_ | 1804138081304969216 |
|---|---|
| adam_text | TABLE OF CONTENTS
Chapter One
GEOMETRIC REPRESENTATION OF
COMPLEX NUMBERS
I. Fundamental Operations
................. 15
1.
Complex coordinate.
2.
Conjugate coordinates.
3.
Exponential form.
4.
Case where
r
is positive.
5.
Vector and complex number.
6.
Addition.
7.
Sub¬
traction.
8.
Multiplication.
9.
Division.
10.
Scalar
product of two vectors.
11.
Vector product of two
vectors.
12.
Object of the course.
Exercises
1
through
11
П.
Fundamental Transformations
............. 26
13.
Transformation.
14.
Translation.
15.
Rotation.
16.
Homothety.
17.
Relation among three points.
18.
Symmetry with respect to a line.
19.
Inversion.
20.
Point at infinity of the Gauss plane.
21.
Product of
one-to-one transformations.
22.
Permutable
trans¬
formations.
23.
Involutoric transformations.
24.
Chan¬
ging coordinate axes.
Exercises
12
through
16
Ш.
Anharmonic Ratio
.................... 35
25.
Definition and interpretation.
26.
Properties.
27.
Case where one point is at infinity.
28.
Real an¬
harmonic ratio.
29.
Construction.
30.
Harmonic qua¬
drangle.
31.
Construction problems.
32.
Equian-
harmonic quadrangle.
Exercises
17
through
31
11
12
contents
Chapter Two
ELEMENTS OF ANALYTIC GEOMETRY IN
COMPLEX NUMBERS
I. Generalities
.......................... 55
33.
Passage to complex coordinates.
34.
Parametric
equation of a curve.
П.
Straight Line
........................ 56
35.
Point range formula.
36.
Parametric equation.
37.
Non-parametric equation.
38.
Centroid of a triangle.
39.
Algebraic value of the area of a triangle.
Exercises
32
through
37
Ш.
The Circle
......................... 63
40.
Non-parametric equation.
41.
Parametric equation.
42.
Construction and calibration.
43.
Particular cases.
44.
Case ad —be
=0. 45.
Example.
Exercises
38
through
45
IV. The Ellipse
......................... 75
46.
Generation with the aid of two rotating vectors.
47.
Construction of the elements of the ellipse.
48.
Theo¬
rem.
49.
Ellipse, hypocycloidal curve.
V. Cycloidal Curves
...................... 83
50.
The Bellermann-Morley generation with the aid of
two rotating vectors.
51.
Theorems.
52.
Epicycloids,
hypocycloids.
VI. Unicursal Curves
..................... 88
53.
Definition.
54.
Order of the curve.
55.
Point
construction of the curve.
56.
Circular unicursal curves.
57.
Foci.
Vu.
Conies
........................... 95
58.
General equation.
59.
Species.
60.
Foci, center.
61.
Center and radius of a circle.
62.
Parabola.
63.
Hy¬
perbola.
64.
Ellipse.
Exercises
46
through
59
CONTENTS 13
УШ.
Unicursal Bicircular Quartics and Unicursal
Cir¬
cular
Cubics ..................... 106
65. General
equation.
66. Double
point.
67. Point
construction of the cubic.
68.
Inverse of a conic.
69.
Limaçon
of Pascal, cardioid.
70.
Class of cubics
and quartics considered.
71.
Foci.
72.
Construction
of the quartic.
Exercises
60
through
71
Chapter Three
CIRCULAR TRANSFORMATIONS
I
.
General Properties of the Homography
........ 126
73.
Definition.
74.
Determination of the homography.
75.
Invariance
of anharmonic ratio.
76.
Circular trans¬
formation.
77.
Conservation of angles.
78.
Product
of two
homographies.
79.
Circular group of the plane.
80.
Definitions.
Exercises
72
through
74
П.
The Similitude Group
.................. 134
81.
Definition.
82.
Properties.
83.
Center of similitude.
84.
Determination of a similitude.
85.
Group of trans¬
lations.
86.
Group of displacements.
87.
Group of
translations and homotheties.
88.
Permutable
simili¬
tudes.
89.
Involutoric similitude.
90.
Application.
Exercises
75
through
83
ΙΠ.
Non-similitude Homography
.............. 145
91.
Limit points.
92.
Double points.
93.
Decomposition
of a homography.
94.
Definitions.
95.
Parabolic homo¬
graphy.
96.
Hyperbolic homography.
97.
Elliptic
homography.
98.
Siebeck s theorem.
Exercises
84
through
91
14
CONTENTS
IV.
Möbius
Involution
.................... 158
99.
Equation.
100.
Sufficient condition.
101.
Properties.
102.
Determination of an involution.
103.
Theorem.
104.
Construction of the involution defined by two pairs
of points AA , BB .
Exercises
92
through
96
V.
Permutable Homographies................
166
105.
Sufficient condition.
106,107.
Theorems.
108.
Har¬
monic involutions.
109, 110.
Theorems. 111. Simul¬
taneous invariant of two
homographies.
112.
Transform
of a homography.
Exercises
97
through
102
VI. Antigraphy
......................... 174
113.
Definition.
114.
Properties.
A. Antisimilitude
175
115.
Equation.
116.
Properties.
117.
Symmetry.
118.
Double points.
119.
Construction of the double
point E.
Exercises
103
and
104
B.
Non-
Antisimilitude Antigraphy
179
120.
Circular transformation.
121.
Limit points.
122.
In¬
version.
123.
Non-involutoric
antigraphies.
124.
Elliptic
antigraphy.
125.
Hyperbolic antigraphy.
126.
Sym¬
metric points.
127.
Determination of the affix of the
center of a circle by the method of H. Pflieger-Haertel.
128.
Schick s theorem.
Exercises
105
through
112
VO.
Product of Symmetries
................. 193
129.
Symmetries with respect to two lines.
130.
Sym¬
metry and inversion.
131.
Product of two inversions.
132.
Homography obtained as product of inversions.
133.
Antigraphy obtained as product of three symmetries.
Assorted exercises
113
through
136
Index
............................... 206
|
| adam_txt |
TABLE OF CONTENTS
Chapter One
GEOMETRIC REPRESENTATION OF
COMPLEX NUMBERS
I. Fundamental Operations
. 15
1.
Complex coordinate.
2.
Conjugate coordinates.
3.
Exponential form.
4.
Case where
r
is positive.
5.
Vector and complex number.
6.
Addition.
7.
Sub¬
traction.
8.
Multiplication.
9.
Division.
10.
Scalar
product of two vectors.
11.
Vector product of two
vectors.
12.
Object of the course.
Exercises
1
through
11
П.
Fundamental Transformations
. 26
13.
Transformation.
14.
Translation.
15.
Rotation.
16.
Homothety.
17.
Relation among three points.
18.
Symmetry with respect to a line.
19.
Inversion.
20.
Point at infinity of the Gauss plane.
21.
Product of
one-to-one transformations.
22.
Permutable
trans¬
formations.
23.
Involutoric transformations.
24.
Chan¬
ging coordinate axes.
Exercises
12
through
16
Ш.
Anharmonic Ratio
. 35
25.
Definition and interpretation.
26.
Properties.
27.
Case where one point is at infinity.
28.
Real an¬
harmonic ratio.
29.
Construction.
30.
Harmonic qua¬
drangle.
31.
Construction problems.
32.
Equian-
harmonic quadrangle.
Exercises
17
through
31
11
12
contents
Chapter Two
ELEMENTS OF ANALYTIC GEOMETRY IN
COMPLEX NUMBERS
I. Generalities
. 55
33.
Passage to complex coordinates.
34.
Parametric
equation of a curve.
П.
Straight Line
. 56
35.
Point range formula.
36.
Parametric equation.
37.
Non-parametric equation.
38.
Centroid of a triangle.
39.
Algebraic value of the area of a triangle.
Exercises
32
through
37
Ш.
The Circle
. 63
40.
Non-parametric equation.
41.
Parametric equation.
42.
Construction and calibration.
43.
Particular cases.
44.
Case ad —be
=0. 45.
Example.
Exercises
38
through
45
IV. The Ellipse
. 75
46.
Generation with the aid of two rotating vectors.
47.
Construction of the elements of the ellipse.
48.
Theo¬
rem.
49.
Ellipse, hypocycloidal curve.
V. Cycloidal Curves
. 83
50.
The Bellermann-Morley generation with the aid of
two rotating vectors.
51.
Theorems.
52.
Epicycloids,
hypocycloids.
VI. Unicursal Curves
. 88
53.
Definition.
54.
Order of the curve.
55.
Point
construction of the curve.
56.
Circular unicursal curves.
57.
Foci.
Vu.
Conies
. 95
58.
General equation.
59.
Species.
60.
Foci, center.
61.
Center and radius of a circle.
62.
Parabola.
63.
Hy¬
perbola.
64.
Ellipse.
Exercises
46
through
59
CONTENTS 13
УШ.
Unicursal Bicircular Quartics and Unicursal
Cir¬
cular
Cubics . 106
65. General
equation.
66. Double
point.
67. Point
construction of the cubic.
68.
Inverse of a conic.
69.
Limaçon
of Pascal, cardioid.
70.
Class of cubics
and quartics considered.
71.
Foci.
72.
Construction
of the quartic.
Exercises
60
through
71
Chapter Three
CIRCULAR TRANSFORMATIONS
I
.
General Properties of the Homography
. 126
73.
Definition.
74.
Determination of the homography.
75.
Invariance
of anharmonic ratio.
76.
Circular trans¬
formation.
77.
Conservation of angles.
78.
Product
of two
homographies.
79.
Circular group of the plane.
80.
Definitions.
Exercises
72
through
74
П.
The Similitude Group
. 134
81.
Definition.
82.
Properties.
83.
Center of similitude.
84.
Determination of a similitude.
85.
Group of trans¬
lations.
86.
Group of displacements.
87.
Group of
translations and homotheties.
88.
Permutable
simili¬
tudes.
89.
Involutoric similitude.
90.
Application.
Exercises
75
through
83
ΙΠ.
Non-similitude Homography
. 145
91.
Limit points.
92.
Double points.
93.
Decomposition
of a homography.
94.
Definitions.
95.
Parabolic homo¬
graphy.
96.
Hyperbolic homography.
97.
Elliptic
homography.
98.
Siebeck's theorem.
Exercises
84
through
91
14
CONTENTS
IV.
Möbius
Involution
. 158
99.
Equation.
100.
Sufficient condition.
101.
Properties.
102.
Determination of an involution.
103.
Theorem.
104.
Construction of the involution defined by two pairs
of points AA', BB'.
Exercises
92
through
96
V.
Permutable Homographies.
166
105.
Sufficient condition.
106,107.
Theorems.
108.
Har¬
monic involutions.
109, 110.
Theorems. 111. Simul¬
taneous invariant of two
homographies.
112.
Transform
of a homography.
Exercises
97
through
102
VI. Antigraphy
. 174
113.
Definition.
114.
Properties.
A. Antisimilitude
175
115.
Equation.
116.
Properties.
117.
Symmetry.
118.
Double points.
119.
Construction of the double
point E.
Exercises
103
and
104
B.
Non-
Antisimilitude Antigraphy
179
120.
Circular transformation.
121.
Limit points.
122.
In¬
version.
123.
Non-involutoric
antigraphies.
124.
Elliptic
antigraphy.
125.
Hyperbolic antigraphy.
126.
Sym¬
metric points.
127.
Determination of the affix of the
center of a circle by the method of H. Pflieger-Haertel.
128.
Schick's theorem.
Exercises
105
through
112
VO.
Product of Symmetries
. 193
129.
Symmetries with respect to two lines.
130.
Sym¬
metry and inversion.
131.
Product of two inversions.
132.
Homography obtained as product of inversions.
133.
Antigraphy obtained as product of three symmetries.
Assorted exercises
113
through
136
Index
. 206 |
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| dewey-raw | 512.7/88 |
| dewey-search | 512.7/88 |
| dewey-sort | 3512.7 288 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Dover ed., 1. publ. |
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| id | DE-604.BV035109412 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:16:56Z |
| indexdate | 2024-07-09T21:22:31Z |
| institution | BVB |
| isbn | 9780486466293 0486466299 |
| language | English French |
| lccn | 2007042751 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016777269 |
| oclc_num | 175218175 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 208 S. graph. Darst. 22 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Dover Publications |
| record_format | marc |
| series2 | Dover books on mathematics |
| spelling | Deaux, Roland Verfasser aut Introduction à la géométrie des nombres complexes Introduction to the geometry of complex numbers Roland Deaux. Transl. by Howard Eves Dover ed., 1. publ. Mineola, NY Dover Publications 2008 208 S. graph. Darst. 22 cm txt rdacontent n rdamedia nc rdacarrier Dover books on mathematics Nachdr. der Ausg. Ungar, New York, 1956 Numbers, Complex Geometry, Projective Komplexe Zahl (DE-588)4128698-4 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s Komplexe Zahl (DE-588)4128698-4 s DE-604 http://www.loc.gov/catdir/enhancements/fy0809/2007042751-d.html Publisher description Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016777269&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Deaux, Roland Introduction to the geometry of complex numbers Numbers, Complex Geometry, Projective Komplexe Zahl (DE-588)4128698-4 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4128698-4 (DE-588)4020236-7 |
| title | Introduction to the geometry of complex numbers |
| title_alt | Introduction à la géométrie des nombres complexes |
| title_auth | Introduction to the geometry of complex numbers |
| title_exact_search | Introduction to the geometry of complex numbers |
| title_exact_search_txtP | Introduction to the geometry of complex numbers |
| title_full | Introduction to the geometry of complex numbers Roland Deaux. Transl. by Howard Eves |
| title_fullStr | Introduction to the geometry of complex numbers Roland Deaux. Transl. by Howard Eves |
| title_full_unstemmed | Introduction to the geometry of complex numbers Roland Deaux. Transl. by Howard Eves |
| title_short | Introduction to the geometry of complex numbers |
| title_sort | introduction to the geometry of complex numbers |
| topic | Numbers, Complex Geometry, Projective Komplexe Zahl (DE-588)4128698-4 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Numbers, Complex Geometry, Projective Komplexe Zahl Geometrie |
| url | http://www.loc.gov/catdir/enhancements/fy0809/2007042751-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016777269&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT deauxroland introductionalageometriedesnombrescomplexes AT deauxroland introductiontothegeometryofcomplexnumbers |