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Audin M. — Geometry
Audin M. — Geometry



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Название: Geometry

Автор: Audin M.

Аннотация:

This is a book written for students who have been taught a small amount of geometry at secondary school and some linear algebra at university. It comes from several courses I have taught in Strasbourg.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 363

Добавлена в каталог: 24.12.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
action      145 190
Aerial      263
Affine conic      185
Affine frame      12
Affine group      19 35 40
Affine independence      12 33
Affine isometry      44 59
Affine line      10
Affine mapping      14
Affine plane      10
Affine projection      33
Affine property      260
Affine quadric      185
Affine space      7
Affine subspace      10
Affine vs projective      147 159 200 210
Affinity      36
Alternated      117
Alternated bilinear form      244
Alternating group      106 130 133 140
Anallagmatic invariant      108 241
Angle at the circumference      74
Angle of a plane rotation      55 78
Angle of a rotation      115
Angle of a similarity      81
Angle of two curves      85
Angle of two planes      121
Angle, geometric      71
Angle, oriented      1
Angle, oriented (of lines)      68
Angle, oriented (of vectors)      66
Antarctic      135
Anti-rotation      114 116
Apex      271
Apollonius      2 236 238
Apparent contour      299
Arc length      261
Archimedian      137
Area of a spherical triangle      121
Area of a time zone      120
Area, signed      119 286
Astroid      254 266
Asymptote      191 260
Axiom, parallel      2 13 122 181
Axis of a proper conic      193
Axis of a rotation      113 115
Axis of revolution      269
Axis of the Earth      135
Axis, focal      194
Axis, major      193
Axis, minor      193
Axis, radical      92 107 217 224
Ball      see "Football"
Banach      136
Barycenter      26
Barycenter, preservation of      17
Barycentric coordinates      36 119 178
Base, locus      206
Base, point      94
Basis, direct      60
Basis, orthogonal      226
Basis, orthonormal      52
Bathroom      136
Beethoven      126
Belgian story      238
bernoulli      262
bezout      207
Bifocal property      195
Bilinear form      43 225
Bilinear form, alternated      244
Bilinear form, symmetric      225
Biruled surface      239
bisector      196
Bisector, external      72
Bisector, internal      71
Bisector, perpendicular      47
Bisectors      70 199 219
black      135
Bonnet      294
Bowl      263 see
Brianchon      243
Canonical      see "Natural"
Cardioid      254 263
Cartan      242
Cartan, decomposition of      242
Cartesian coordinates      12 30
Cartesian equations      31
Cartesian parametrization      274
Catenary      299
Cauchy      44 58
Caustic      249 258 263 264
Center of a conic      188
Center of a quadric      188 214
Center of a rotation      78
Center of a similarity      80
Center of an excircle      see "Excenter"
Center of curvature      256
Center of gravity      27 see
Center of the circumcircle      see "Circumcenter"
Center of the incircle      see "Incenter"
Central, conic      188
Central, dilatation      16
Central, quadric      188
Centroid      27
Ceva      38
Chasles      8 68 208 244
Chessboard      174
Cicumradius      110
circle      193 216
Circle of Euler      1 61 111 267
Circle, great      120
Circle, inversion      84
Circle, nine point      62 see
Circle, osculating      256 266
Circle, small      120
Circular group      167 224
Circular helix      265
Circular points      216
Circumcenter      61
circumcircle      61
Circumradius      98
Classification      189 193 204 226
Common perpendicular      131
Compactness of the ellipse      191 193
Compactness of the group O(n)      52
Compactness of the projective space      144
Compactness of the sphere      140
Complement of a conic      244
Complement of a hyperplane      40
Complement of a line      36 40 170
Complete quadrilateral      38 61
Completion, projective      149 164 200
Complex exponential      54
Complex numbers, use in plane geometry      79 82 99 164
Cone      243 271 289
Cone of revolution      238 270
Cone, isotropy      200
Confocal, conies      243
Confocal, family      244
Confocal, quadrics      244
Conic, affine      185 189
Conic, central      188
Conic, confocal      243
Conic, degenerate in a pencil      207
Conic, projective      200
Conic, proper      190
Conic, real      244
Conic, section      238
Conic, tangential      243
Conjugacy      100
Conjugated diameters      236
Conjugation      21 35
Conjugation, principle of      21
Connectedness of $GL(n;R)^{+}$      63
Connectedness of $O^{+}(n)$      57
Connectedness of the ellipse      191
Connectedness of the parabola      193
Connectedness of the projective space      144
Conoid of Pluecker      296
Constrained extrema      298
Convex      28 122
Convex, hull      29 122
coordinates      12
Coordinates, barycentric      36 119 178
Coordinates, Cartesian      12 30
Coordinates, homogeneous      157 179
Cosine      55
Criteria for congruence      103
Criteria for similarity      106
Cross product      see "Vector product"
Cross-ratio and orthogonality      216
Cross-ratio and permutations      164
Cross-ratio of four collineal points      161
Cross-ratio of four lines      172
Cross-ratio of four points on a conic      209
Cross-ratio, computation      162
Cross-ratio, preservation of the      161
Cross-ratio, real      166
cube      128
Cubic, cuspidal      251 258 261
Cubic, nodal      261
Cubic, real      244
Cup of coffee      249 see
Curvature of a cone      289
Curvature of a cylinder      289
Curvature of a plane      289
Curvature of a plane curve      255
Curvature of a space curve      265
Curvature of a torus of revolution      299
Curvature of Gauss      287
Curvature of surfaces of revolution      299
Curvature of the sphere      122 124 289
Curvature, algebraic      255
Curvature, center      256
Curvature, direction of      290
Curvature, principal      290
Curvature, radius      256
Curve      258
Curve, cycloidal      252
Curve, parallel      257
Curve, parametrized      247
Curve, regular      258
Cusp      299
Cusp, point      258
Cuspidal, cubic      251 258 261
Cyclic group      130
Cyclic points      76
Cyclicity      75 166
Cycloid      265
Cycloidal curve      252
Cylinder      271 289
Cylinder of revolution      270
Decomposition of Cartan      242
Decomposition, polar      242
Desargues      26 39 151 154 176
Descartes      264
Diagonalization of real symmetric matrices      233
Diagonalization, simultaneous      189 230 234 285
Diameters of a circle      223
Diameters, conjuated      236
Diffeomorphism      85
Differential of a mapping      85 111 280
Dihedral group      130 132 141
Dilatation      16 35
Dimension of a projective space      143
Dimension of an affine space      8
Direct basis      60
Direct similarity      80 165
Direction of an affine space      8
Direction of curvature      290
Directrix      194 219
Discriminant      263 274 299
Discriminant of a quadratic form      241
Distance on the sphere      138
Distance, Euclidean      44
Distance, hyperbolic      181
Distance, intrinsic      138
dodecahedron      128 139
Dot product      see "Scalar product"
Double line      185 192 207
Double vector product      131
Dual of a conic      243
Dual of a convex      136
Dual of a polyhedron      125 136
Dual of a quadric      243
Duality and polarity      203
Duality between convex subsets      136
Duality between polyhedra      125
Duality, projective      153 172 242
Duerer      2 128 143 249
Earth      2 122 135 176
Easter Island      126
Eccentricity      194
EDGE      123
ellipse      190 211 266
Ellipsoid      214 269
Elliptic integral      339
Elliptic paraboloid      214
Elliptic point      283 290
Envelope      199 248 299
Envelope of normals      257
Envelope of the Simson lines      266
Epicycloid      253 264
Equation of a quadric      184
Equation, Cartesian      31
Equation, parametric      30
Equation, reduced      193
Equibarycenter      26
Erdoes      102
Euclid      2 7
Euclidean affine space      44
Euclidean vector space      44
Euler      61 110 111 123 284 293
Evolute      257
Evolute of a catenary      299
Evolute of a cycloid      265
Evolute of a parabola      266
Evolute of an ellipse      266
Excenter      98
Excircle      98
Exponential, complex      54
External bisector      72
extrema      295
Face      123
Fagnano      101
Family of lines      249
Family, confocal      244
Fermat      105
Feuerbach      110
Finite subgroup      130
Finite subgroup of $O^{+}(3)$      130 140
First criterion for congruence      103
First criterion for similarity      106
First fundamental form      287
First theorem of Apollonius      236
Flex      259
Focal axis      194
Focus      194 218
Football      see "Soccer"
Form, bilinear alternated      244
1 2 3
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