Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Verdina J. — Projective Geometry and Point Tranformations
Verdina J. — Projective Geometry and Point Tranformations

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Projective Geometry and Point Tranformations

Автор: Verdina J.

Аннотация:

This volume aims to present projective geometry as a particular case in the study of point transformations. The approach used in this volume has been successfully used in the classroom and the author is convinced of its merits.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 206

Добавлена в каталог: 30.08.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Abelian group      5
Affine mapping      55
Algebraic curves      170
Algebraic hypersurface, equation      13
Algebraic hypersurface, order      13
Algebraic varieties      13
Angle between two surfaces      160
Asymptotes      96
Axial pencil      23
Axis of coordinates      2
Base points of a pencil of conies      107
Bezout's theorem      170
Bilinear form      88
Birational transformation      127 132
Bitangent conics      189
Bundle of lines      23
Bundle of planes      23
Canonic equations      65
Characteristic invariant      65
Characteristic invariant of the homothety      77
Characteristic roots      60
Circular inversion      133 See
Circular points at infinity      18
Cofactor      166
Collinear points      15
Collineation between homogeneous spaces      6
Collineation between projective planes      47
Collineation between projective planes, any two corresponding lines intersect at the axis      69
Collineation between projective planes, any two corresponding points are collinear with the center      68
Collineation between projective planes, definition      48
Collineation between projective planes, determined by four pairs of corresponding points      54
Collineation between projective planes, determined by three pairs of corresponding lines and a pair of corresponding points      56 57
Collineation between projective planes, verification that a given collineation is a special homology      66
Collineation between projective spaces      47 80 82
Collineation between projective spaces, as a product of two polarities      103 104
Collineation between projective spaces, between homogeneous spaces      6
Collineation between projective spaces, definition      80
Collineation between projective spaces, determined as a product of two polarities      85
Collineation between projective spaces, equations      81
Collineation between projective spaces, tangent to another collineation      153
Collineations between superposed planes, characteristic equation      60
Collineations between superposed planes, characteristic roots      60
Collineations between superposed planes, determination of its fixed points and fixed lines      84
Collineations between superposed planes, determined by two fixed points and two points which correspond doubly      72
Collineations between superposed planes, fixed points      60
Commutative group      5
Complete plane quadrangle      52
Complete plane quadrangle, diagonal points      52
Complete plane quadrangle, diagonal triangle      52
Complete plane quadrangle, opposite sides      52
Complete plane quadrangle, sides      52
Complete plane quadrangle, vertices      52
Complete quadrilateral      51
Complex number      179
Complex number, conjugate of      179
Complex point      17
Configuration      23
Conformal transformation      160
conic      87
Conic, as a pair of lines      88
Conic, base points      107
Conic, bitangent      189
Conic, degenerate      88 90
Conic, determined by five points      89
Conic, discriminant      88
Conic, equation      87
Conic, equations of a conic satisfying given conditions      190
Conic, fundamental      101
Conic, its intersection with a line      90
Conic, through five given points      190
Conic, through four points and tangent to a given line      191
Conics, iperosculating      189
Conics, osculating      189
Conics, pencil      106
Conics, pencil of conies bitangent to a given conic      193
Conics, pencil of conies tangent to a given conic      193
Conjugate points with respect to a conic      98
Connection      111
Connection between two planes      118
Connection between two planes, algebraic      119
Connection between two planes, orders      119
Contact of order n between curves      115
Contact of order n between curves, analytic condition      115
Contact, invariance under a point transformation      121
Contact, projective character      116
Contacts between plane curves      115
Coordinates, homogeneous      3
Coordinates, homogeneous projective      7
Coordinates, nonhomogeneous      3
Correlation between projective planes      47 77
Correlation between projective planes, definition      77
Correlation between projective planes, determined by four points mapping into four lines      79
Correlation between projective planes, equation      77
Correlation between projective planes, involutory      78
Correlation between projective planes, represented by a bilinear equation      78
Correlation between projective planes, verification that a given correlation is involutory      79
Correlation between projective spaces      82
Correlation between projective spaces, definition      82
Correlation between projective spaces, equations      83
Correlation between projective spaces, incidence quadric      83
Correlation between projective spaces, null correlation      83 86
Correlation between projective spaces, polarity      83
Correlation between projective spaces, represented by a bilinear equation      83
Correspondence, identity      4
Correspondence, product      4
Cramer's rule      171
Cremona transformation      127 128
Cremona transformation, between r-dimensional spaces      160
Cremona transformation, between three-dimensional spaces      159
Cross ratio      30 See
Cubic surface as a transform of a plane      158
Cubic transformation      157
Cubic transformation, equations      157
Cubic transformation, singular points      158
Cubic transformation, transform of a plane      158
Curve      2 161
Curve, double point      112
Curve, isolated point      112
Curve, multiple points      111
Curve, node      112
Curve, simple point      111
Curve, triple point      112
Curve-cusp      112
Curves, algebraic      170
Curves, contacts      114
Curves, osculating at a point      115
Curves, tangent at a point      115
Curves, touching at a point      115
Cyclic points      18
Degenerate conic      88 90
Degenerate conic, a conic is degenerate if its discriminant is equal to zero      91
Degenerate conic, method to determine the two distinct lines if the discriminant rank is 2      92
Degenerate conic, the two lines which compose a degenerate conic are coincident if and only if the rank of the discriminant is equal to 1      92
Degenerate pencil of conics      187
Degenerate pencil of conics, there are three degenerate conies in a pencil      187
Desargues, involution theorem      108
Desargues, theorem on the homological triangle      68
Determinant, cofactor      166
Determinant, defined      165
Determinant, emi-symmetric      167
Determinant, Laplace development      166
Determinant, minor      166
Determinant, properties      167
Determinant, skew-symmetric      167
Diagonal lines      52
Diagonal triangle      52
Distance      162
Double point of a curve      112
Double ratio      30
Double ratio of four lines      30
Double ratio of four numbers      30
Double ratio of four points      29
Double ratio, it is invariant under a projectivity      32
Double ratio, its permutation effect      34
Dual definitions      24
Duality      23
Duality, plane      25
Duality, space      24
Equations, homogeneous      169
Equations, parametric      2
Euclidean space      162
Euler's theorem      184
Field      178
Field, complex      178
Finite points      16
Fixed lines under the homology      60 61
Fixed points under a collineation, their determination      60
Fixed points under a projectivity, their determination      38
Fixed points under the homology      60
Flat pencil      23
Forms, geometric      23
Fourth harmonic      30
Function      181
Function, complex      181
Function, homogeneous      183
Function, inverse      182
Function, one-to-one      182
Function, real      181
Fundamental conic      101
Fundamental points      47
Fundamental pyramid      3
Fundamental theorem      33 53
Fundamental triangle      47
Geometric forms      23
Geometry, Riemannian      164
Graphic properties      22
Group      4
Group, commutative (abelian)      5
Group, continuous      6
Group, dimension      6
Group, finite      5
Group, infinite      5
Group, order      5
Group, permutable elements      5
Harmonic homology      70
Harmonic range      30
Homogeneous coordinates      16
Homogeneous function      183
Homogeneous function, example      183
Homogeneous Plueckerian coordinates      11
Homogeneous, equations      169
Homography      6 See
Homology      60
Homology, axis      60
Homology, canonic equation      65
Homology, characteristic invariant      65
Homology, construction of the corresponding line to a given line if the center, the axis, and two corresponding points are given      74
Homology, construction of the corresponding point to a given point if the center, the axis, and two corresponding points are given      74
Homology, determined by its center, axis, and characteristic      73
Homology, harmonic      70
Homoloidal net of conies      130
Homothety      76
Homothety, its characteristic invariant      77
Hyperplane      2
Hyperplanes of projective spaces      10
Hyperplanes of the coordinates      2
Hypersurfac, algebraic      13
Hypersurfac, irreducible      13
Hypersurfac, reducible      13
Hypersurface      161
Ideal points      16
Identity      4
Imaginary lines      17
Imaginary points      17
Incidence conic      101
Incidence quadric      83
Incidence quadric, equations      83 84
Indeterminate tangent line to a conic      96
Intrinsic metric geometry      164
Invariant, characteristic      65
Inversion in the complex plane      130
Inversion in the complex plane, singular points      130
Inversion in the real plane      133
Inversion in the real plane, circle of inversion      134
Inversion in the real plane, exceptional point      135
Inversion in the real plane, pole      133
Inversion in the real plane, power      133
Inversion in the real plane, transformation of plane curves      135
Inversion in the real space      159
Inversion in the real space, center of inversion      160
Involution      40
Involution, center      43
Involution, conjugate points      41
Involution, determined by its center and power      44
Involution, double points      41
Involution, metric property      43
Involution, power      44
Involutory correlation      78
Iperosculating conies      189
Irreducible algebraic hypersurface      13
Isotropic line      18
Jacobian      184
Knotted parabola      112
Line      12
Line at infinity      16
Line coordinates      20
Line, complex      2
Line, definition      1
Line, homogeneous      3
Line, real      2
Linear subspaces, equations      11
Linear subspaces, line      12
Linear subspaces, plane      12
Linearly dependent points      8
Mapping      181
Mappings, product      183
Matrix      168
Matrix, rank      168
Metric properties      22
Motions      161
Motions, definition      161
Motions, equations      161
Multiple point of a curve      111
Multiple roots of an equation      170
Net of conies      130
Nondegenerate conic      93
Nondegenerate conic tangent to the x-axis      94
Nondegenerate conic, definition      93
Nondegenerate conic, determination of the asymptotes      96
Nondegenerate conic, property      93
Nonhomogeneous Plueckerian coordinates      11
One-dimensional form      23
One-to-one correspondence      183
Origin      1
Osculating circle of a conic      195
Pappus theorem      52
Parabola, knotted      112
Parameters      197
Parametric representation of rational algebraic curves      123
Parametric representation of the ellipse      123
Parametric representation of the hyperbola      124
Parametric representation of the parabola      124
Pencil of conies      106
Pencil of conies, bitangent to a given conic      193
Pencil of conies, degenerate      187
Pencil of conies, iperosculating a given conic      195
Pencil of conies, osculating a given conic      194
Pencil of conies, tangent to a given conic at one of its points      193
Pencil of lines      23 174
Plane      12
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте