Audin M. — Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Audin M. — Geometry

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Название: Geometry

Автор: Audin M.

Аннотация:

Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michèle Audin, professor at the university of Strasbourg has written a book allowing them to remedy this situation and, and starting from linear algebra extend their knowledge of affine, euclidian and projective geometry, conic and quadric sections, curves and surfaces. It includes many nice theorems like the nine-point circle, Feuerbach's theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for each exercise are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master's level to discover geometry and deepen their knowledge and understanding.

Язык:

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 357

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Poincare      181 293
Point at infinity      91 148 164 167 186 221
Point of Fermat      105
Point of Gergonne      134
Point of inflexion      259
Point, base      94
Point, circular      216
Point, cusp      258
Point, elliptic      283 290
Point, hyperbolic      283 290
Point, limiting      94
Point, parabolic      284 298
Point, planar      284 298
Point, regular      258 273
Point, singular      258 273 274 277 298
Point, weighted      26
Polar decomposition      242
Polar form      225
Polar hyperplane      203
Polar ocean      135
Polar of a point with respect to a conic      203 240
Polarity with respect to a quadric      203
Pole of a hyperplane with respect to a quadric      203
Pole of a line with respect to a conic      203
Pole of an inversion      84
Pole, north      134
Polyhedron      122
Polyhedron, dual      125
Polyhedron, Platonic      2 128
Polyhedron, regular      126
Porism of Steiner      109
Position of a curve with respect to its tangent      259
Position of a parabola with respect to its tangent      236
Position of a surface with respect to its tangent plane      282
Position of an ellipse with respect to its tangent      191
Position, general      280
Positive definite quadratic form      43
Power of a point with respect to a circle      89
Power of an inversion      84
Preservation of alignment      156
Preservation of angles      70 71 81 83 86 111 165
Preservation of barycenter      17
Preservation of circles      91 166
Preservation of collinearity      16 41 179
Preservation of orientation      50 60
Preservation of orthogonality      44 86
Preservation of the cross-ratio      161
Preservation of the norm      44
Preservation of the scalar product      44
Principal curvature      290
Principle of conjugation      21
Principle of Huygens      257 274
Problem of Fagnano      101
Product, scalar      43 215 225
Product, vector      117
Projection in projective geometry      see "Perspectivity"
Projection, affine      33
Projection, stereographic      134 140 164
Projective completion      149 159 164 200 210
Projective conic      200
Projective duality      153 172 242
Projective frame      157 178
Projective group      156 165 204
Projective hyperplane      145 146
Projective line      143 147 164
Projective plane      143 148
Projective quadric      200
Projective reader      185
Projective space      143
Projective subspace      145
Projective transformation      155 204
Projective transformation (of the line)      159 165
Proper affine quadric      185
Proper projective quadric      200
Property, affine (of a curve)      248 260
Property, bifocal      195
Property, global      248 293
Property, local      248 293
Property, metric      215 248 293
Property, monofocal      194
Property, tangential (of conics)      196 199 243 249
Pseudosphere      299
Ptolemy      108
Punctual masses      26
Pyramid      126 132
Pythagoras      98
Quadratic form      43 225 283
Quadric      184 269
Quadric at infinity      238
Quadric degenerate in a pencil      207
Quadric in dimension 3      234
Quadric, affine      185 234
Quadric, central      188
Quadric, confocal      244
Quadric, projective      200
Quadric, proper affine      185
Quadric, proper projective      200
Quadric, real      234 239
Quadrilateral, complete      38 61
Quaternions      141
Radical axis      92 107 217 224
Radius of the circumcircle      110 see
Radius of the incircle      110
Radius, curvature      256
Rain      2 264
Rainbow      2 249 264
Range, harmonic      164
Rank of a quadratic form      227 234
Rank of a skew-symmetric matrix      245
Ratio of a dilatation      16
Ratio of a similarity      79
Real conic      244
Real cubic      244
Real quadric      234 239
Rectangular hyperbola      193
Reduced equation      193
Reflection      46 59 222
Reflection, glide      77 116
Regular point      258 273
Regular polygon      126
Regular polyhedron      126
Regular surface      273
Relation of Euler      110
Relation, metric (in the triangle)      98
Revolution      269
Riemann      164 293
Rigid motion      50 58
Rotation in space      113
Rotation, plane      55 78
Rotatory reflection      114 116
Rule, parallelogram      9
Rule, slide      1
Ruled surface      234 239 270 296 297
Ruler      176
Saddle      234 298
Saddle, horse      271 283
Saddle, monkey      298
Scalar product      43 215
Scalar, function of Leibniz      60
Schmidt      62
Schwarz      44 58 180
Schwarz lemma      180
Screw displacement      116
Second criterion for congruence      103
Second criterion for similarity      106

Second fundamental form      287
Second theorem of Apollonius      236
Second theorem of Desargues      176
Section, conic      238
Separation      135
Signature of a quadratic form      228
Signed area      119 286
Similarity, criteria for      106
Similarity, direct      80 165
Similarity, linear      79
Similarity, opposite      80
Simple group      137
Simplicity of       137
Simson      104 see
Sine      55
Singular point      258 273 274 277 298
Skew-symmetric bilinear form      244
Skew-symmetric matrix      245
Slide rule      1
Small circle      120
Snell      264
soccer      137
Space, affine      7
Space, projective      143
Space, tangent      201
Spanned affine subspace      11
Spanned projective subspace      147
Sphere      120 164 289
Sphere of Riemann      164
Spherical triangle      120 138
Spherical trigonometry      138
Spilett      135
Steiner      104 109 208 see
Stereographic projection      134 140 164
Strip of Moebius      300
Structure of isometries      46
Structure transport of      9 67
Subspace, affine      10
Subspace, generated      11 147
Subspace, projective      145
Subspace, spanned      11 147
Subspaces, parallel      12
Sum of the angles of a triangle      73 122 182
Summit      298
Sun      135 248 264
Support of a geometric surface      272
surface      272
Surface of revolution      269 296
Surface, geometric      272
Surface, parametrized      272
Surface, regular      273
Surface, ruled      234 239 270 296 297
Swallow tail      274
Sylvester      228
Symmetric bilinear form      43 225
Symmetric group      130 133
Symmetric matrix      225 233
Symmetry      34
Symmetry, orthogonal      45
Tangent hyperplane      201
Tangent mapping      280
Tangent plane      277
Tangent space      201
Tangent to a central conic      199
Tangent to a conic      188 243
Tangent to a curve      248 258 279
Tangent to a parabola      198
Tangent to a quadric      186
Tangent vector      258
Taylor      259 283
Tetrahedron, regular      128 132
Tetrahedron, scalene      36 133
Thales      1 23 34 173
Theorem of Apollonius      236
Theorem of Bezout      207
Theorem of Brianchon      243
Theorem of Ceva      38
Theorem of Chasles      244
Theorem of Chasles and Steiner      208
Theorem of Desargues      26 39 151 154
Theorem of Desargues (second)      176
Theorem of Erdoes and Mordell      102
Theorem of Euler      285 289
Theorem of Feuerbach      1 110
Theorem of Gauss and Bonnet      294
Theorem of Hahn and Banach      136
Theorem of Jacobi      244
Theorem of Jordan      248
Theorem of Liouville      83 111
Theorem of Menelaues      38 39 108 209
Theorem of Miquel      104 177
Theorem of Pappus      25 39 150 176 240
Theorem of Pascal      103 108 209 240
Theorem of Pythagoras      98
Theorem of Thales      1 23 34 173
Theorem of the four vertices      248
Theorem of the six cross-ratios      176
Theorem of Weierstrass      314
Theorem of Witt      213 231
Theorem of zeroes      238
Theorem, fundamental      41 179
Theorem, implicit function      247 277 281
Theorem, Inverse Function      276
Theorem, remarkable of Gauss      291
Theorema egregium      291
Third criterion for congruence      103
Time Zone      120
Topology of       142 180
Topology of the linear group      63
Topology of the orthogonal group      52
Topology of the projective space      144
Topology of the real projective plane      179
Torsion      265
Torus of revolution      270 299
Tractrix      299
Transformation, projective      155
Translation      16
Transport by conjugation      21
Transport of structure      9 67
TRANSPOSE      52
Triangle, hyperbolic      182
Triangle, inequality      44 58
Triangle, spherical      120 138
Triangle, strict inequality      58
Trigonometry, plane      98
Trigonometry, spherical      138
Type of a conic      193
Umbilic      300
Umbrella of Whitney      298
Underlying vector space      8
Using complex numbers      57 79 82 99 164 215
Vector space, Euclidean      44
Vector, isotropic      225 226
Vector, normal      254 284
Vector, tangent      258
Vectorialization      9
Vertex      123 248
Vertex of a cone      271
Vertex of a parabola      193
Vinci      128 137
Vosges      298
Wave-front      258
Weierstrass      314
Whitney      298
Witt      213 231
Zeugma      4 178

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