Geometry of conics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2007
|
| Series: | Mathematical world
26 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | VII, 134 S. Ill., graph. Darst. |
| ISBN: | 0821843230 9780821843239 |
Staff View
MARC
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| 240 | 1 | 0 | |a Geometričeskie svojstva krivych vtorogo porjadka |
| 245 | 1 | 0 | |a Geometry of conics |c A. V. Akopyan ; A. A. Zaslavsky |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2007 | |
| 300 | |a VII, 134 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vu
Chapter
1.
Elementary Properties of Curves of Second Degree
1
1.1.
Definitions
1
1.2.
Analytic definition and classification of curves
of second degree
5
1.3.
The optical property
6
1.4.
The
isogonal
property of conies
10
1.5.
Curves of second degree as projections of the circle
15
1.6.
The eccentricity and yet another definition of conies
17
1.7.
Some remarkable properties of the parabola
19
Chapter
2.
Some Results from Classical Geometry
27
2.1.
Inversion and Feuerbach s theorem
27
2.2.
Basic facts about
projective
transformations
29
2.3.
Some facts from the geometry of the triangle
38
2.4.
Radical axes and pencils of circles
57
Chapter
3.
Projective
Properties of Conies
65
3.1.
The cross-ratio of four points on a curve. Parametrization. The
converses of Pascal s and Brianchon s theorems
65
3.2.
Polar correspondence. The duality principle
68
3.3.
Pencils of curves. Poncelet s theorem
78
Chapter
4.
Euclidean Properties of Curves of Second Degree
99
4.1.
Special properties of equilateral hyperbolas
99
4.2.
Inscribed conies
105
4.3.
Normals to conies. Joachimstahl s circle
113
4.4.
The
Poncelet
theorem for confocal ellipses
115
vi
CONTENTS
Chapter
5.
Solutions to the Problems
119
Bibliography
131
Index
133
|
| adam_txt |
Contents
Preface
vu
Chapter
1.
Elementary Properties of Curves of Second Degree
1
1.1.
Definitions
1
1.2.
Analytic definition and classification of curves
of second degree
5
1.3.
The optical property
6
1.4.
The
isogonal
property of conies
10
1.5.
Curves of second degree as projections of the circle
15
1.6.
The eccentricity and yet another definition of conies
17
1.7.
Some remarkable properties of the parabola
19
Chapter
2.
Some Results from Classical Geometry
27
2.1.
Inversion and Feuerbach's theorem
27
2.2.
Basic facts about
projective
transformations
29
2.3.
Some facts from the geometry of the triangle
38
2.4.
Radical axes and pencils of circles
57
Chapter
3.
Projective
Properties of Conies
65
3.1.
The cross-ratio of four points on a curve. Parametrization. The
converses of Pascal's and Brianchon's theorems
65
3.2.
Polar correspondence. The duality principle
68
3.3.
Pencils of curves. Poncelet's theorem
78
Chapter
4.
Euclidean Properties of Curves of Second Degree
99
4.1.
Special properties of equilateral hyperbolas
99
4.2.
Inscribed conies
105
4.3.
Normals to conies. Joachimstahl's circle
113
4.4.
The
Poncelet
theorem for confocal ellipses
115
vi
CONTENTS
Chapter
5.
Solutions to the Problems
119
Bibliography
131
Index
133 |
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| discipline | Mathematik |
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| id | DE-604.BV023305462 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:48:17Z |
| indexdate | 2024-07-09T21:15:27Z |
| institution | BVB |
| isbn | 0821843230 9780821843239 |
| language | English |
| lccn | 2007060841 |
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| physical | VII, 134 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical world |
| series2 | Mathematical world |
| spelling | Akopjan, Arsenij V. Verfasser aut Geometričeskie svojstva krivych vtorogo porjadka Geometry of conics A. V. Akopyan ; A. A. Zaslavsky Providence, RI American Math. Soc. 2007 VII, 134 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical world 26 Aus dem Russ. übers. Geometry, Analytic Plane Curves, Algebraic Kegelschnitt (DE-588)4125170-2 gnd rswk-swf Geometrische Methode (DE-588)4156715-8 gnd rswk-swf Kegelschnitt (DE-588)4125170-2 s Geometrische Methode (DE-588)4156715-8 s DE-604 Zaslavskij, Aleksej A. Verfasser aut Mathematical world 26 (DE-604)BV004574320 26 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016489841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Akopjan, Arsenij V. Zaslavskij, Aleksej A. Geometry of conics Mathematical world Geometry, Analytic Plane Curves, Algebraic Kegelschnitt (DE-588)4125170-2 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| subject_GND | (DE-588)4125170-2 (DE-588)4156715-8 |
| title | Geometry of conics |
| title_alt | Geometričeskie svojstva krivych vtorogo porjadka |
| title_auth | Geometry of conics |
| title_exact_search | Geometry of conics |
| title_exact_search_txtP | Geometry of conics |
| title_full | Geometry of conics A. V. Akopyan ; A. A. Zaslavsky |
| title_fullStr | Geometry of conics A. V. Akopyan ; A. A. Zaslavsky |
| title_full_unstemmed | Geometry of conics A. V. Akopyan ; A. A. Zaslavsky |
| title_short | Geometry of conics |
| title_sort | geometry of conics |
| topic | Geometry, Analytic Plane Curves, Algebraic Kegelschnitt (DE-588)4125170-2 gnd Geometrische Methode (DE-588)4156715-8 gnd |
| topic_facet | Geometry, Analytic Plane Curves, Algebraic Kegelschnitt Geometrische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016489841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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