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Audin M. — Geometry
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Название: GeometryАвтор: 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: 2003Количество страниц: 357Добавлена в каталог: 16.04.2005Операции: Положить на полку |
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Предметный указатель
Form, fundamental 287 Form, fundamental (first) 288 Form, fundamental (second) 287 Form, homogeneous 185 Form, polar 225 Form, quadratic 43 225 283 Form, quadratic (positive definite) 43 Form, symmetric bilinear 43 225 Formula of Euler 123 293 Formula of Girard 121 293 Formula of spherical trigonometry 138 Formula of Taylor 259 283 Formula to compute the cross-ratio 162 Formula, class 140 Formulas of Frenet 265 Frame, affine 12 Frame, projective 157 178 frenet 265 Function, holomorpic 165 Function, implicit 247 277 281 Function, scalar of Leibniz 60 Fundamental first form 287 Fundamental second form 287 Fundamental theorem 41 179 Gauss 229 285 291 293 Gauss mapping 286 Gauss, curvature 287 Generated affine subspace 11 Generated projective subspace 147 Geodesic 300 Geometric surface 272 Geopolitical 135 Gergonne 134 Girard 121 293 Glide reflection 77 116 Global property 248 293 Golden number 139 Gram 62 Gram — Schmidt orthonormalization process 62 Grassmann 177 Grassmannian 177 Great circle 120 Group action 2 40 190 204 Group of a polyhedron 130 Group of dilatations 35 Group of isometries 44 Group of isometries of a figure 99 100 106 132 133 263 Group of Lorentz 63 Group of projective transformations 156 165 Group of similarities 80 Group of the cube 133 141 Group of the dodecahedron 139 141 Group of the tetrahedron 133 141 Group operation see "Group action" Group, affine 19 40 Group, affine (of the line) 35 Group, alternating 106 130 133 140 Group, circular 167 224 Group, cyclic 130 132 140 Group, dihedral 130 132 141 Group, linear 19 63 Group, orthogonal 52 Group, projective 156 165 204 Group, simple 137 Group, symmetric 130 133 Hahn 136 Half-plane 36 39 59 Half-plane of Poincare 181 293 Half-turn 115 Harmonic pencil 172 219 Harmonic range 164 Heart 254 263 Helicoid 296 300 Helix, circular 265 Hexagon 137 182 209 243 Hexagram, mystic 209 hilbert 7 238 Hobson 135 Holomorphic function 165 Holomorphic mapping 111 Homogeneous coordinates 157 179 Homogeneous form 185 Homography 155 159 165 208 Horse saddle see "Mountain pass" Hull, convex 29 122 Huygens 257 274 Hyperbola 190 211 Hyperbola, rectangular 193 Hyperbolic distance 181 Hyperbolic geometry 182 Hyperbolic paraboloid 214 234 271 Hyperbolic plane 182 Hyperbolic point 283 290 Hyperbolic triangle 182 Hyperboloid 269 Hyperboloid of one sheet 214 296 Hyperboloid of revolution 296 Hyperboloid of two sheets 214 Hyperplane at infinity 149 160 Hyperplane, polar 203 Hyperplane, projective 145 146 Hyperplane, tangent 201 Hypocycloid 253 264 Hypocycloid, three-cusped 1 253 263 265 267 icosahedron 129 Image of a quadric 185 Incenter 98 incircle 98 Inequality of Cauchy and Schwarz 44 58 Inequality of Ptolemy 108 Inequality, isoperimetric 248 Inequality, triangle 44 Inequality, triangular (on the sphere) 138 Inertia law 228 infinity 91 148 150 159 164 221 Inflexion point 259 Inradius 110 Integral, elliptic 339 Internal bisector 71 Intersecting pencil 94 Intersection of a plane and a cone 238 Intersection of a quadric and a line 186 Intersection of two circles 217 Intersection of two conics 207 Intersection of two lines 145 Intersection of two surfaces 247 281 Invariant, anallagmatic 241 inversion 84 134 167 222 Inversion, circle 84 Involution 34 84 175 Island, Easter 126 Island, mysterious 135 Isometry group 44 Isometry, affine 44 59 Isometry, linear 44 59 Isoperimetric inequality 248 Isosceles triangle 99 Isotropic vector 225 226 Isotropy cone 200 225 jacobi 244 JORDAN 248 Kepler 237 Kidney 254 Kinematics 247 Latitude 135 Law of Descartes 264 Law of inertia of Sylvester 228 Law of Kepler 237 Law of Snell 264 Leibniz 60 Lemniscate of Bernoulli 262 Length, arc 261 Limiting point 94 Line at infinity 148 151 152 210 216 Line contained in a quadric 239 Line of Simson 1 104 177 238 248 266 Line of Steiner 104 238 267 Line, affine 10 149 178 Line, complex projective 164 Line, double 185 192 207 Line, normal to a curve 256 Line, projective 143 147 164 Line, real projective 164 Linear group 19 63 Liouville 83 111 Local property 248 293 Locus, base 206 longitude 135 Lorentz 63 Major axis 193 Manifold 293 MAP 2 122 135 139 Maple 297 Mapping, affine 14 Mapping, Gauss 286 Mapping, holomorphic 111 Mapping, tangent 280 Masses, punctual 26 Matrix of a quadratic form 225 233 Matrix, skew-symmetric 245 Matrix, symmetric 225 233 Measure 70 Menelaues 38 39 209 Meridian 120 135 270 Metamorphosis 153 Method of Gauss 229 Metric property 215 248 293 midpoint 27 Minor axis 193 Miquel 104 177 Moebius 180 300 Moebius strip 180 Monge 283 Monofocal property 194 Mordell 102 Morley 267 Motion of planets 237 Motion, science in 2 Mountain pass 271 see Multiplication of theorems 154 Mystic hexagram 209 Napoleon 105 Natural 8 Negative isometry 50 Nephroid 254 263 Newton 2 38 264 Nine point circle see "Circle of Euler" Nodal cubic 261 Nondegenerate 188 226 Nondegenerate quadratic form 226 Norm 44 Normal to a curve 256 Normal vector 254 284 North 134 Notation of Monge 283 Nullstellensatz 185 238 Number, golden 139 Ocean, polar 135 octahedron 129 132 Odyssey 126 One point compactification 140 148 Opposite similarity 80 Optics 249 258 263 Orientation 60 Orientation of lines in space 114 179 Oriented angle 1 66 68 orthocenter 61 176 Orthogonal basis 226 Orthogonal group 52 Orthogonal of a pencil 95 Orthogonal of a subspace 43 203 Orthogonal pencils 95 96 Orthogonal vectors 43 226 Orthogonality 43 226 236 Orthogonality of two circles 89 173 Orthogonality of two pencils of circles 95 Orthogonality of two subspaces 43 Orthogonalization 226 Orthogonalization, simultaneous 189 230 234 285 Orthonormal basis 52 Orthonormalization 62 Osculating circle 256 266 Pappus 25 39 150 176 parabola 192 211 249 266 Parabolic aerial 263 Parabolic point 284 298 Paraboloid 269 Paraboloid, elliptic 214 Paraboloid, hyperbolic 214 234 271 parallel 12 120 135 145 270 Parallel axiom 2 13 122 181 Parallel curves 257 Parallel subspaces 12 Parallelogram 9 32 Parallelogram, rule 9 Parallels, nonexistence of 122 145 PARAMETER 193 Parametrization of a circle 261 Parametrization of a conic 208 261 Parametrization of a curve 247 Parametrization of a cuspidal cubic 261 Parametrization of a hyperbola 236 Parametrization of a nodal cubic 261 Parametrization of an algebraic curve 248 Parametrization of the ellipse 191 Parametrization, Cartesian 274 Parametrized curve 247 Parametrized surface 272 Pascal 103 108 209 240 Pencil 93 Pencil of circles 92 217 239 Pencil of conics 207 239 244 Pencil of lines 171 208 Pencil of quadrics 206 244 Pencil of real conics 239 Pencil, harmonic 172 219 Pencil, intersecting 94 Pencil, nonintersecting 94 Pencil, tangent 95 Pentagon 128 137 139 Perec 1 Perpendicular bisector 47 59 Perpendicular bisector, hyperbolic 182 Perpendicular bisector, hyperplane 59 Perpendicular bisector, projective 143 148 Perpendicular bisector, real projective 179 Perpendicular bisector, rotation 78 Perpendicular bisector, tangent 277 Perpendicular bisector, tangent to a ruled surface 297 Perpendicular bisector, tangent to a surface of revolution 297 Perrin 177 Perspective 2 143 174 Perspectivity 171 176 photography 176 Pivot 104 177 Planar point 284 298 Plane, affine 10 Planet 237 Platonic solids 2 128 Pluecker 177 215 296
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