Weeks J.R. — The shape of space :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Weeks J.R. — The shape of space

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: The shape of space

Автор: Weeks J.R.

Аннотация:

This friendly textbook explores many of the possible answers to the question, "What is the universe shaped like?" It provides an overview of the basic geometry of two- and three-dimensional spaces, illustrating the connection between geometry, cosmology, and the behavior of the physical universe. Numerous illustrations, exercises, and thought-experiments are included. Technical language and mathematical equations are kept to a minimum.

Язык:

Рубрика: Математика/Популярные издания/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 2002

Количество страниц: 382

Добавлена в каталог: 04.05.2005

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

Предметный указатель

# symbol      75
$H^{2}\times E$ geometry      244—247 250—251
$K^{2}\times S^{1}$       58—59 248
$K^{2}\times S^{1}$ as a bundle      232
$K^{2}\times S^{1}$ , as a product      91
$K^{2}\times S^{1}$ , circles in the sky of      306
$K^{2}\times S^{1}$ , surfaces in      128
$K^{2}\times S^{1}$ , view in      104—107
$K^{3}$       237 250
$P^{2}\times S^{1}$       96 250
$S^{2}\times E$ geometry      243—245 250
$S^{2}\times S^{1}$       91—97 250
1/2 turn manifold      108 249
1/3 turn manifold      123 231 249
1/4 turn manifold      107—109 229—233 249
1/6 turn manifold      123 231 249
3/4 turn manifold      108
Abbreviations for manifolds      73—75
Admit a geometry      164
Aliens, extracosmic      215
Ancient Greeks      279
Angle-sum of hyperbolic triangle      154—156
Angle-sum of spherical triangle      136—144
Antipodal triangle      140
Area of hyperbolic triangle      154—156
Area of spherical triangle      136—144
Aristotle      279
Astria      4
Ball      200—201
big bang      259—260 262—263 265—267 295—296
Big bang, correct picture      267
Big bang, incorrect picture      266
Big bang, philosophical aspects      273—278
Biplanes      13—14 99—103 113—114
Blackbody spectrum      298—299
Bundle      229—242 251—255
CAP      365
Cell-division      166—169
Chess on a Klein bottle      50 53—55
Chess on a torus      17—20
China      279
Circles in the sky      295—308
Classes of geometries      246—248
Closed manifold      42—44
CMB      see "Cosmic microwave background"
COBE      see "Cosmic background explorer"
Cone point      118—122 157—159
Connected sum      65—81
Connected sum, definition      70
Conway      362
Cornish      306
Cosmic background explorer      298—299
Cosmic crystallography      285—293
Cosmic microwave background      297—302 307
Cross surface      374—375
Cross surface, double      375
Cross surface, triple      375
Crosscap      365—366
Crosshandle      364
Crosshandle in presence of crosscap      372—373
Crosshandle, homeomorphic to two crosscaps      370—372
Curvature      149—151 175—184
Curvature, Gaussian      181
Curvature, measurement of      37 182 208—210 269—271
Curvature, sectional      244—247
Cusp      43—44
Cylinder      83—84
de Sitter      282
Democritus      279
Dodecahedral spaces      219—224
Double cross surface      375
Double disk method      201—205
Double lune      139—141
Double torus      374
Doughnut surface      9 30
Doughnut surface with cusp      43—44
Dyck's surface      375
Dyck's Theorem      372—373
Einstein      261—262 281—282
Elliptic geometry      135—147 199—212
Elliptic geometry for Poincare dodecahedral space      220—224
Elliptic geometry on a surface      157—158 162—164
Elliptic geometry, definition      149—150
Elliptic geometry, sample three-manifolds      248
Euclidean geometry, definition      149—150
Euclidean geometry, list of three-manifolds      248—249
Euler number      165—185 374
Euler number, definition      174
Euler number, general description      165
Expansion of the universe      260—263 265—269
Extrinsic property      31—35
Flat geometry      120—122
Flat surfaces and three-manifolds      99—124 273
Flat torus      13—20 23—24
Flatland      3—4 187S
Flatland story, beginning      3—9
Flatland story, continuation      45—47
Flatland story, ending      65—69
Four dimensions      187—197
Friedmann      261—262 282
Galaxies      260—261 289
Galaxies, catalogs of      292—293
Gauss      37 208—210
Gauss — Bonnet formula      165—184
Gauss — Bonnet formula for elliptic geometry      174
Gauss — Bonnet formula for Euclidean geometry      175
Gauss — Bonnet formula for hyperbolic geometry      174
Gauss — Bonnet formula for surfaces of constant curvature      181
Gauss — Bonnet formula for surfaces of varying curvature      182—184
Gaussian curvature      181
Geocentric universe      279—280
Geodesic      37 136
Geometry      26—29
Geometry, Relativity and the Fourth Dimension      190—192 195—197
Girard      137
Global geometry      41
Global property      39—41
Global topology      40—41
Gluing      13
God      275
Great circle      136—137
Great two-sphere      203 207
Half turn manifold      108 249
Half turn manifold, surfaces in      128
Handle      363
Handle in presence of crosscap      372—373
Hexagonal three-torus      122—123
Hexagonal torus      111—120
Hinton      4
Homeomorphic surfaces      362
Homogeneity      41—42
Homogeneity of the Universe      263—264
Homogeneous geometry      41—42 149—150
Homogeneous geometry on surfaces      157—164
Homogeneous geometry on three-manifolds      219—228 243—255
Homogeneous three-manifold      96
Hubble      262
Hubble, constant      262 264
Hyperbolic 3-manifolds      219—221 249—250 273
Hyperbolic 3-manifolds, cosmic crystallography in      291
Hyperbolic geometry      149—156 213—218
Hyperbolic geometry for "typical" three-manifolds      249—250
Hyperbolic geometry for Seifert — Weber space      219—221
Hyperbolic geometry for surfaces      157—164
Hyperbolic geometry, definition      149—151
Hyperbolic geometry, Thurston's work      249—250 255
Hyperbolic n-gon      170
Hyperbolic paper      151—154
Hyperbolic plane      149—156
Hyperbolic space      213—218 282

Hyperbolic triangle      154—156 214—216
Hypersphere      201—210
Intrinsic point of view      38—39
Intrinsic property      31—39
Isotropic geometry      244—246
Isotropic three-manifold      96
Isotropy of the microwave background      299—300
Isotropy of the Universe      263—265
Jungle gym in a nonorientable three-manifold      58—59
Jungle gym in a three-torus      21—22
Jungle gym, twisted Euclidean      251—253
Klein      280
Klein bottle      48—58
Klein bottle in four-dimensional space      191
Klein bottle, chess on      50 53—55
Klein bottle, cosmic crystallography in      290—292
Klein bottle, cut into two pieces      74
Klein bottle, limerick      73
Klein bottle, solid      236
Klein bottle, three-dimensional analog of      237
Klein bottle, tic-tac-toe on      50—54
Klein perforation      371
Knotted sphere      193—195
Lachieze-Rey      287
Last scattering surface      301—308
Lehoucq      287
Lemaitre      262
Leucippus      279
Light-year      260
Local geometry      40—41
Local property      39—41
Luminet      287
Lune, double      139—141
Manifold      11
Manifold, precise definition      40—41
Manifold-with-boundary      42
MAP      see "Microwave anisotropy probe"
Microwave anisotropy probe      307—308
Microwave background radiation      297—302 307
Milky Way      260
Mirror reversal      45—49
Mirror reversal and orientability      58
Moebius bridge      371
Moebius strip      47—49 125—126
Moebius strip, two-sided      129
Multiconnected space      280
n-gon      169—170
Negative curvature      151
Nonhomogeneous      41
Nonorientable manifold      58
Octahedral space      227
One-dimensional manifold      41
One-sided surface      125—131
One-sided surface, definition of      125
Open manifold      42—44
Ordinary surface      368
Orientable manifold      58
Orientation-reversing path      58
Pair separation histogram      290—291
Patchwork quilt      368
Penzias      297
Perforation      367
Planck satellite      307—308
plasma      295—297
Poincare conjecture      280
Poincare dodecahedral space      220—224 248
Poincare dodecahedral space, circles in the sky of      306
Positive curvature      149
PRODUCT      83—97
Product, geometrical      86—88 91
Product, multiplication      86
Product, three-dimensional      89—97
Projective plane      59—64
Projective plane, minus a disk      70—73
Projective plane, nomenclature      374
Projective three-space      62—64 210—212 248 282
Puncto      135
Quarter turn manifold      107—110 229—233 249
Quarter turn manifold, circles in the sky of      306
Quarter turn manifold, cosmic crystallography in      291
Quaternionic manifold      226—227
RADIANS      136
Riemann      280
Rubber band with twist      31—33
Schwarzschild      280
Sectional curvature      244—247
Seifert — Weber space      219—221 224 249
Seifert — Weber space, circles in the sky of      306
Sheep      86
Solid $K^{3}$       237
Solid $S^{2}\times S^{1}$       237
Solid doughnut      236
Solid Klein bottle      236
Solve geometry      254—255
Spacetime      195—197 272—278
Spergel      306
Sphere      135—147 199—200
Sphere vs. ball      200—201
Sphere, knotted      193—195
Sphereland      135—136
Spherical 3-manifolds      219—224 273
Spherical 3-manifolds, cosmic crystallography in      292
Spherical n-gon      169—170
Spherical triangle      136
Spherical triangle, area and angles      136—144
Spirits      190—193
Starkman      306
Superclusters      289—293
Surfaces      11
Surfaces, classification of      361—375
Surfaces, Classification Theorem      368
Surfaces, nonredundant list of      80
Surfaces, ordinary      368
Surfaces, redundant list of      76
Surfaces, triangulated      367
Telescope      280
Tetrahedral space      226—227
Three-manifold, formal definition      40
Three-manifold, informal definition      11
Three-sphere      199—210 248 280 282
Three-torus      20—24 249
Three-torus as a product      89—91
Three-torus, circles in the sky of      302—306
Three-torus, how corners fit      224—225
Three-torus, introduced to astronomers      280—281
Three-torus, oblong      41
Three-torus, view in      103—105
Thurston      249 255
Tic-tac-toe on a Klein bottle      50—54
Tic-tac-toe on a torus      14—17 103
topology      26—31
Torus, $S^{1}\times S^{1}$       84—85 87
Torus, chess on      17—20
Torus, double      374
Torus, drawn as a doughnut surface      9 30
Torus, flat      13—20 23—24
Torus, flat torus vs. doughnut surface      30—31 41
Torus, hexagonal      111—120
Torus, three-dimensional      see "Threetorus"
Torus, tic-tac-toe on      14—17 103
Torus, triple      374
Torus, twisted      239—241 252—253
Triangle, Euclidean      144
Triangle, hyperbolic      154—156 214—216
Triangle, spherical      136—144
Triangulated surface      367
Triple cross surface      375
Triple torus      374
Twisted $H^{2}\times E$ geometry      254
Twisted $S^{2}\times E$ geometry      254

1 2

О проекте