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Barbeau E.J. — Mathematical Fallacies, Flaws and Flimflam
Barbeau E.J. — Mathematical Fallacies, Flaws and Flimflam

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Название: Mathematical Fallacies, Flaws and Flimflam

Автор: Barbeau E.J.


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.
Newspapers are responsible for a good number of these mathematical mishaps, particularly in arithmetic (especially percentages) and probability. Quite a number of the "fallacies" come from professional mathematicians. Some are the result of simple oversight, and others are deliberately crafted by the mathematician to drive home an important point to students.
A glimpse at the Table of Contents offers examples from number theory, algebra and trigonometry, geometry, finite mathematics, probability, calculus, linear algebra, and advanced undergraduate mathematics.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 167

Добавлена в каталог: 17.11.2009

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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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