Yaglom I.M. — Complex Numbers in Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Yaglom I.M. — Complex Numbers in Geometry

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Название: Complex Numbers in Geometry

Автор: Yaglom I.M.

Аннотация:

This book is intended for pupils in the top classes in high schools and for students in mathematics departments of universities and teachers' colleges. It may also be useful in the work of mathematical societies and may be of interest to teachers of mathematics in junior high and high schools.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 253

Добавлена в каталог: 17.02.2013

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

Предметный указатель

Absolute      110 114 120
angle      29 112
Angle of parallelism      184
Angle, between circles      137
Antiaxis      82 120
Antihomography      131
Antihomography, axial      157
Antiparallel lines      80 120
Antipole      110
Apollonius circle      (see Circle of Apollonius)
Argument      5 17 20
Associated triangle of quadrangle      79 150
Axial circular geometry      171
Axial circular transformation      157 171
Axial circular transformation of Lobachevskii plane      188—194
Axial inversion      164
Axial inversion of first kind      190
Axial inversionof fourth kind      194
Axial inversionof second kind      191
Axial inversionof third kind      191
Axial symmetries      193
Axis      (see Oriented line)
Axis of similitude      105
Bundle of circles      157
Cayley transformation      188
Center of inversion      141
Center of similitude      104
Central circle      36—39
Central point      36—39
Centroid      52
circle      112 124
Circle at infinity      114 124
Circle of Apollonius      49
Circular geometry      143
Circular transformation of Lobachevskii plane      180
Compatible transformations      190
Complementary segment      185
Complex numbers, double      13 18—21
Complex numbers, dual      12 14—18
Complex numbers, ordinary      1—7
Conformal transformation      138 181
Conjugate numbers      3 15 18
Cosine Theorem      152
Cross-ratio of angles between four lines      163 189
Cross-ratio of distances between four points      138 181
Cross-ratio of four lines      93
Cross-ratio of four points      32
CYCLE      112 124 Horocycle Equidistant
Dilatation      29
Dilatation, axial      166 242
Direct transformation      (see Homography)
Director circle      39 176
Director point      40
Distance      29 111
Divisors of zero      16 19 119
Double numbers      13 18—21
Dual numbers      12 14—18
Equianharmonic quadrangle      76
Equianharmonic tetrad      76
Equidistant curve      112 124
Equidistantial transformation      162
Euler circle      52
Euler line      52
Fundamental theorem of algebra      7
Generalized complex numbers      7 10
Half-turn      (see Symmetry about point)
Harmonic quadrangle      74 147
Harmonic quadrilateral      107 173
Harmonic tetrad      74 107
Homography      131
Homography, axial      157
Homothety      (see Dilatation)
Horocycle      112

Hyperbolic cosine      20
Hyperbolic sine      20
Hypercomplex numbers      22—25
Identical transformation      132
Imaginary number      1
Invariance of cross-ratio      133
Inverse of transformation      132
inversion      139
Inversion of first kind      182
Inversion of second kind      183
Inversion of third kind      184
Inversion, unit      139
Isodynamic centers      77
Laguerre transformation      (see Axial circular transformation)
Liebmann transformation      187
Linear transformation      131
Linear-fractional transformation      (see Homography Antihomography)
Lines at infinity      120
Mobius transformation      (see Ordinary circular transformation Circular
Modulus      3 15 18
Most general complex numbers      10—14
Motions      29 83—89 111 123 158
Net of circles      175
Nine-points circle      52
Octaves      25
Opposite transformation      (see Anti-homography)
Ordinary circular transformation      130—145
Oriented angle      28 31 80 88 112 123
Oriented angle, between circles      137
Oriented angle, between cycles      180
Oriented circle      90
Oriented distance      80 88 123
Oriented length      80
Oriented line      30
Oriented point      111
Oriented tangential distance      162
orthocenter      50
Orthogonal circles      152
Parallel displacement      (see Translation)
Parallel lines      80
Pencil of equal inclination      124
Poincare model      109—117 188
Point(s) at infinity      34 110
Polar axis      81
Polar coordinates      81
Pole      81
Power of line with respect to circle      99 101 175
Power of point with respect to circle      44 155
Product of transformations      132
Ptolemy’s theorem      148
Quaternions      24
Radical axis      47
Radical center      48
Ratio of three points      30
Real axis      26
Reflection      (see Symmetry about line)
Reorientation      83 111 123 158
reversion      193
Rotation      28 85—87
Simson line      63
Spiral similarity      28 131
Symmetry about line      27 83 111 123 131 158
Symmetry about point      27 83 111 123 131 158
Symmetry to equidistant curve      187
Symmetry to horocycle      184
Symmetry with respect to circle      140 141 183
Tangential distance      161
Translation      28 83—85 131
Trigonometrical form      6
Ultrainfinite points      124
Ultraparallel lines      118
Unit circle      26
Unit inversion      (see Inversion)

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