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



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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
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Предметный указатель
Plane of lines      23
Plane of points      23
Plane polarity      101
Plane, definition      1
Plane, homogeneous      3
Plueckerian coordinates of the line      20
Point at infinity      16
Point transformation      119 145
Point transformation, approximating another point transformation      122
Point transformation, between two r-dimensional spaces      155
Point transformation, characteristic curves      149
Point transformation, characteristic directions      148
Point transformation, characteristic projectivities      150
Point transformation, invariance of the contact      121
Point transformation, Jacobian      146
Point transformation, neighborhood of a pair of corresponding points      146
Point transformation, neighborhood of the rth-order      146
Point transformation, osculating another point transformation      153
Point transformation, osculating projectivity      121 122
Point transformation, quadratic transformations osculating a point transformation      155
Point transformation, regular pair of corresponding points      146
Point transformation, tangent      153
Point transformation, transformations which approximate others      152
Point, definition      1
Point, finite      16
Point, fundamental      3
Point, multiple      111
Point, real      2
Point, unit point      3
Points common to two conies      105
Polar line      99
Polarity as an involutory correlation      101
Polarity, plane      101
Pole      99
Principle of duality      23
Projective character of the contact      116
Projective plane      24
Projective spaces      7 23
Projectivity between directional pencils      147
Projectivity between lines      27
Projectivity between lines, characteristic invariant      39
Projectivity between lines, elliptic projectivity      39
Projectivity between lines, equations      27
Projectivity between lines, fixed points      38
Projectivity between lines, hyperbolic projectivity      39
Projectivity between lines, involution      40
Projectivity between lines, modulus      28
Projectivity between lines, parabolic projectivity      39
Projectivity between lines, the fundamental theorem      33
Projectivity between lines, united points      38
Projectivity between lines, vanishing points      39
Projectivity osculating a point transformation      121
Pyramid, fundamental      3
Quadratic transformation      127
Quadratic transformation of the first kind      131
Quadratic transformation of the second kind      131
Quadratic transformation of the third kind      131
Quadratic transformation, a line is transformed into a conic through the singular points      131
Quadratic transformation, definition      127
Quadratic transformation, equations      127
Quadratic transformation, equations in reduced form      141
Quadratic transformation, it transforms a point into a conic      129
Quadratic transformation, osculating a point transformation      155
Quadratic transformation, preserving ratios of corresponding areas      141
Quadratic transformation, singular lines      130 131
Quadratic transformation, singular points      129—131
Quadrics      13
Quadrilateral in the projective plane      51
Quadrilateral in the projective plane, definition of      51
Range of points      23
Rank of matrix      168
Rational algebraic curves      123
Rational algebraic curves, definition      123
Reducible algebraic hypersurface      13
Riemannian geometry      164
Riemannian space      164
Riemannian variety      163
Sets      177
Similitude      163
Simple polygons      51
Singular points of a quadratic transformation      129
Singular points of the inversion in the complex plane      130
Singular projectivity      28
Space, complex      2
Space, definition      1
Space, Euclidean      162
Space, homogeneous      2
Space, n-dimensional homogeneous space      2
Space, n-dimensional space      1
Space, nonhomogeneous space      2
Space, projective      7
Space, real      2
Space, Riemannian      163
Special homology      60
Steiner, theorem      107
Subspaces, intersection of      12
Subspaces, skew      12
Subspaces, union of      12
Superposed lines      28
Superposed spaces      4
surface      2 161
Tangent collineations      153
Tangent line, indeterminate      96
Tangents to a conic      90
Tangents to a conic at a double point      114
Tangents to a conic at a multiple point      114
Tangents to a conic at a simple point      95
Tangents to a conic from a point      97
Tangents to a curve at the origin      113
Transformation      181
Transformation of projective coordinates      8
Transformation, birational      127 132
Transformation, conformal      160
Transformation, Cremona      127
Transformation, cubic      157 See
Transformation, group      4
Transformation, point transformation      111 119
Transformation, point transformation, algebraic      120
Transformation, point transformation, degenerate      120
Transformation, quadratic      127
Transformation, rational      132
Triangle in the projective plane      51
Triangle in the projective plane, definition      51
Triangle in the projective plane, sides      51
Triangle in the projective plane, vertices      51
Triple point of a curve      112
Two-dimensional forms      23
Unit point      47
Vanishing lines      55
Variety      161
Variety, k-dimensional      2
Variety, linear      161
Variety, parametric equations      161
Variety, Riemannian      163
Variety, t-dimensional linear      2
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