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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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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 conics 243 Confocal family 244 Confocal quadrics 244 Conic degenerate in a pencil 207 Conic section 238 Conic, affine 185 189 Conic, central 188 Conic, confocal 243 Conic, projective 200 Conic, proper 190 Conic, real 244 Conic, tangential 243 Conjugacy 100 Conjugated diameters 236 Conjugation 21 35 Conjugation, principle of 21 Connectedness of 63 Connectedness of 57 Connectedness of the ellipse 191 Connectedness of the parabola 193 Connectedness of the projective space 144 Conoid of Plucker 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 radius 256 Curvature, algebraic 255 Curvature, center 256 Curvature, direction of 290 Curvature, principal 290 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 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
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