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Akopyan A.V., Zaslavsky A.A. — Geometry of conics. Mathematical world
Akopyan A.V., Zaslavsky A.A. — Geometry of conics. Mathematical world



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Название: Geometry of conics. Mathematical world

Авторы: Akopyan A.V., Zaslavsky A.A.

Аннотация:

The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confocal ellipses. The book demonstrates the advantage of purely geometric methods of studying conics. It contains over 50 exercises and problems aimed at advancing geometric intuition of the reader. The book also contains more than 100 carefully prepared figures, which will help the reader to better understand the material presented


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 134

Добавлена в каталог: 10.03.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Asymptotes of a hyperbola      2
Axis of a hyperbola, imaginary      2
Axis of a hyperbola, real      2
Axis of a parabola      2
Axis of an ellipse major      1
Axis of an ellipse minor      1
Axis, radical      57
Brocard angle      49
Circle, Apollonius      41
Circle, Ceva      39
Circle, Euler      28
Circle, Fermat — Apollonius      13
Circle, Joachimstahl's      115
Circle, nine-point      28
Circle, pedal      38
Coaxial circles      58
Complete quadrilateral      109
conic      2 17
Conic section      17
Correspondence, polar      68
Cross-ratio      31 32
Curve of second degree      2 5
Dandelin spheres      17
Directrix      18
Duality principle      36
Eccentricity      18
ellipse      1
Ellipse, Brocard      48
Ellipse, Steiner, circumscribed      53 107
Ellipse, Steiner, inscribed      52
Hyperbola      2
Hyperbola, Apollonius      114
Hyperbola, equilateral      2 99
Hyperbola, Feuerbach      103
Hyperbola, Kiepert      104
inversion      27
Involution      93
Isogonal conjugate      12
Isogonal conjugation      41 87
Isotomic conjugation      56 88
Lemma, Simson's      22
Line, Aubert      109
Line, Gauss      88 109
Line, Simson's      23
normal      113
parabola      2 19
Pencil      78
Pencil of circles      58
Pencil of circles, elliptic      58
Pencil of circles, hyperbolic      58
Pencil of circles, parabolic      58
Perspector      105
Point, Apollonius      53
Point, Brocard      48
Point, Feuerbach      29
Point, Gergonne      55
Point, isogonal conjugate      41
Point, Lemoine      46
Point, limit, of a pencil of circles      59
Point, Miquel      109
Point, Nagel      55
Point, Torricelli      54
polar      35 68
Polar correspondence      35
Polar curve      70
Polar, trilinear      36
Pole      35 68
Pole, trilinear      36
Power of a point      57
Radical center      58
Symmedian      46
Theorem on pencils of conics      78
Theorem, Brianchon's      33 63
Theorem, Brianchon's, converse      66
Theorem, Desargues'      32
Theorem, Droz — Farny      111
Theorem, Emelyanov and Emelyanova      103
Theorem, Feuerbach's      28
Theorem, four conics      85
Theorem, four conics, dual to      87
Theorem, Fregier      76 96
Theorem, Monge's      90
Theorem, Newton's      36
Theorem, Pappus'      32
Theorem, Pascal's      33 45
Theorem, Pascal's, converse      65
Theorem, Poncelet      61 67 93 115 124
Theorem, Sondat's      125
Theorem, three conics      86
Theorem, three conics, dual to      87
Triangle, Ceva      39
Triangle, circumcevian      39
Triangle, pedal      38
Triangle, self-polar      74
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