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Barbeau E.J. — Mathematical Fallacies, Flaws and Flimflam
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Название: Mathematical Fallacies, Flaws and FlimflamАвтор: Barbeau E.J. Аннотация: This book is a collection of mathematical mistakes made by students, teachers, and occasionally seasoned researchers, along with an analysis for most of them. While all the material is for personal enlightenment and amusement, high school and college teachers may use the material to illustrate important and subtle points in mathematics.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2000Количество страниц: 167Добавлена в каталог: 17.11.2009Операции: Положить на полку |
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Предметный указатель
Angle of rotation 301 Angle of rotation between two planes 161 Anticommutativity of external multiplication 74 Anticommutativity of external product 74 Area of a bivector 151 Associativity of vector addition 17 Asymptote 201 Bases of opposite signs 102 Bases of the same sign 102 Bases, deformation of 112 Bases, equivalent 115 Basis deformable into a basis 40 Basis of vector space 40 Basis, orthonormal 140 Basis, standard 45 Bessel inequality 139 Bivector 64 65 Bundle of planes 282 Cauchy — Buniakowski inequality 130 Centre of a curve 194 Centre of symmetry 195 circle 226 Cone, directrix of 240 Cone, vertex of 239 Configuration theorems 307 Coordinates of a vector 41 Coordinates, affine 49 Coordinates, polar 178 Coordinates, projective 272 Cross ratios of four points 327 Curve, algebraic of order n 183 Curve, real algebraic 191 Curve, second-degree central 196 Curve, second-degree elliptic-type 202 Curve, second-degree hyperbolic-type 202 Curve, second-degree noncentral 196 Curve, second-degree parabolic-type 202 Cylinder 248 Cylinder, axis of 248 Cylinder, Elliptical 248 Cylinder, hyperbolic 251 Cylinder, imaginary 250 Cylinder, parabolic 252 Desargues theorem 302 Diameters, conjugate 207 Dimension of a vector space 40 Direction, asymptotic 200 Direction, chordwise 206 Direction, nonasymptotic 200 Direction, nonsingular 203 Direction, principal 222 Direction, singular 203 Distance between points 129 Distance from a point to a plane 161 Distance from a point to a straight line 157 ellipse 168 Ellipse, affine 182 Ellipse, centre of 170 Ellipse, directrices of 170 Ellipse, eccentricity of 170 Ellipse, focal distance of 170 Ellipse, focal property of 171 Ellipse, focal radii of 171 Ellipse, foci of 170 Ellipse, major and minor axes of 170 Ellipse, major and minor semiaxes of 170 Ellipse, striction 233 Ellipse, vertices of 170 Ellipsoid 228 Ellipsoid, imaginary 231 Equation of a plane, parametric vector 84 Equation of a straight line, parametric vector 54 Equations of second-degree curves, canonica'affine 185 Expansion of a vector with respect to a basis 41 Families of vectors, linearly equivalent 118 Family of vectors, complete 39 Family of vectors, orthonormal 139 Fixed points of linear fractional transformation 323 Form of a given basis, metric 137 Form, bilinear 135 Form, positive definite 136 Form, quadratic 136 Form, symmetrical 135 Fourier coefficients 138 Geometry, affine 47 Geometry, Euclidean 129 Geometry, projective-affine 260 Gram — Schmidt orthogonalization process 142 Group of automorphisms of an affine space 276 Group of linear fractional transformations 316 Group of projective transformations 316 Group, general linear 275 Half-planes determined by a straight line 62 Hyperbola 172 Hyperbola, affine 182 Hyperbola, asymptotes of 173 Hyperbola, branches of 173 Hyperbola, centre of 174 Hyperbola, directorial property of 175 Hyperbola, directrices of 174 Hyperbola, focal distance of 174 Hyperbola, focal parameter of 174 Hyperbola, foci of 174 Hyperbola, linear eccentricity of 174 Hyperbola, real and imaginary axes of 174 Hyperbola, semiaxes of 174 Hyperbola, vertices of 174 Hyperboloid of one sheet 233 Hyperboloid of two sheets 231 inversion 318 Isometries of a cube 338 Isometries of a regular dodecahedron 340 Isometries of a regular icosahedron 340 Isometries of a regular octahedron 346 Isometries of a tetrahedron 339 Isomorphism of affine spaces 48 Isomorphism of Euclidean vector spaces 143 Isomorphism of vector spaces 43 Isomorphism, coordinate 44 45 Isomorphism, established from the equality of coordinates 45 Line, parallel to a plane 92 Matrix of transition from a basis to a basis 97 Matrix, equivalent 115 Matrix, orthogonal 144 Matrix, proper orthogonal 145 146 Model of affine geometry 262 Motion of Euclidean space 286 Multiplication in a vector space, scalar 128 Multiplier of linear fractional transformation 328 Orientation of a half-plane 107 108 Orientation of a half-space 110 Orientations of vector space 103 Oval 216 parabola 166 Parabola, affine 182 Parabola, axis of 167 Parabola, focal distance of 168 Parabola, focal parameter of 168 Parabola, focus of 168 Parabola, vertex of 167 Paraboloids, elliptical 242 Paraboloids, hyperbolic 243 Parseval's formula 140 Pencil of planes 280 Pencil of straight lines 256 Pencil, ideal 259 Pencil, ordinary 258 Plane, extended 260 Plane, given by a point and a bivector 82 Plane, projective 269 Plane, projective-affine 260 Points of a plane, nonseparated by a straight line 85 86 Points of a space, nonseparated by a plane 87 Poles of rotation of a sphere 334 Product of a bivector by a number 121 Product of a trivector by a number 121 Product of bivectors, external 121 Product, scalar 125 Product, vector 152 Properties of external multiplication, algebraic 73 Radius vector of a point 49 Rotation 295 Sections, conic 242 Set of vectors, linearly dependent 29 Side of a straight line 105 Space, affine 46 Space, arithmetic projective 277 Space, Euclidean point 128 Space, projective 279 Space, projective-affine 278 Space, real-complex 189 Space, vector (affine) oriented 103 Spaces, affine isomorphic 48 Spaces, Euclidean vector 128 Sphere 228 Stereographic projection 314 Straight line, in space 51 52 Subset, linearly (in)dependent 29 Subspace, real 187 Sum of bivectors 70 Sum of trivectors 124 Surface, l-fold ruled 234 Symmetry in a centre O 195 Symmetry with respect to a circle 317 Symmetry with respect to a straight line 319 System of opposite signs 103 System of the same sign 103 System, affine coordinate 49 System, canonical affine coordinate 182 System, rectangular coordinate 141 Tangent 200 Theorem, configuration 307 Theorem, Desargues 302 Theorem, Fano 308 Theorem, Pappus — Brianchon 310 Theorem, Pappus — Pascal 305 Transformations, affine 286 Transformations, elliptical 324 Transformations, hyperbolic 324 Transformations, linear fractional 315 Transformations, loxodromic 325 Transformations, orthogonal 286 Transformations, parabolic 323 Transformations, projective 286 Translation, (parallel) 95 Triangle inequality 131 Unit vector 141 Vector 15 Vector space, associated with an affine space 48 Vector spaces, isomorphic 43 Vector spaces, real-complex isomorphic 188 Vector, complementary to bivector 152 Vector, Euclidean 128 Vector, finite-dimensional 39 Vector, length of 129 Vector, parallel to a bivector 69 Vector, proportional to a vector 35 Vectors, a linear combination of 28 Vectors, a trivial linear combination of 28 Vectors, collinear 35 68 Vectors, coplanar 36 Volume of a parallelepiped, oriented 125 Volume of a trivector 149
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