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Weeks J.R. Ч The shape of space
Weeks J.R. Ч The shape of space

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Ќазвание: The shape of space

јвтор: Weeks J.R.

јннотаци€:

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: en

–убрика: ћатематика/ѕопул€рные издани€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: second edition

√од издани€: 2002

 оличество страниц: 382

ƒобавлена в каталог: 04.05.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
# symbol      75
$H^{2}\times E$ geometry      244Ч247 250Ч251
$K^{2}\times S^{1}$      58Ч59 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      104Ч107
$K^{3}$      237 250
$P^{2}\times S^{1}$      96 250
$S^{2}\times E$ geometry      243Ч245 250
$S^{2}\times S^{1}$      91Ч97 250
1/2 turn manifold      108 249
1/3 turn manifold      123 231 249
1/4 turn manifold      107Ч109 229Ч233 249
1/6 turn manifold      123 231 249
3/4 turn manifold      108
Abbreviations for manifolds      73Ч75
Admit a geometry      164
Aliens, extracosmic      215
Ancient Greeks      279
Angle-sum of hyperbolic triangle      154Ч156
Angle-sum of spherical triangle      136Ч144
Antipodal triangle      140
Area of hyperbolic triangle      154Ч156
Area of spherical triangle      136Ч144
Aristotle      279
Astria      4
Ball      200Ч201
big bang      259Ч260 262Ч263 265Ч267 295Ч296
Big bang, correct picture      267
Big bang, incorrect picture      266
Big bang, philosophical aspects      273Ч278
Biplanes      13Ч14 99Ч103 113Ч114
Blackbody spectrum      298Ч299
Bundle      229Ч242 251Ч255
CAP      365
Cell-division      166Ч169
Chess on a Klein bottle      50 53Ч55
Chess on a torus      17Ч20
China      279
Circles in the sky      295Ч308
Classes of geometries      246Ч248
Closed manifold      42Ч44
CMB      see "Cosmic microwave background"
COBE      see "Cosmic background explorer"
Cone point      118Ч122 157Ч159
Connected sum      65Ч81
Connected sum, definition      70
Conway      362
Cornish      306
Cosmic background explorer      298Ч299
Cosmic crystallography      285Ч293
Cosmic microwave background      297Ч302 307
Cross surface      374Ч375
Cross surface, double      375
Cross surface, triple      375
Crosscap      365Ч366
Crosshandle      364
Crosshandle in presence of crosscap      372Ч373
Crosshandle, homeomorphic to two crosscaps      370Ч372
Curvature      149Ч151 175Ч184
Curvature, Gaussian      181
Curvature, measurement of      37 182 208Ч210 269Ч271
Curvature, sectional      244Ч247
Cusp      43Ч44
Cylinder      83Ч84
de Sitter      282
Democritus      279
Dodecahedral spaces      219Ч224
Double cross surface      375
Double disk method      201Ч205
Double lune      139Ч141
Double torus      374
Doughnut surface      9 30
Doughnut surface with cusp      43Ч44
Dyck's surface      375
Dyck's Theorem      372Ч373
Einstein      261Ч262 281Ч282
Elliptic geometry      135Ч147 199Ч212
Elliptic geometry for Poincare dodecahedral space      220Ч224
Elliptic geometry on a surface      157Ч158 162Ч164
Elliptic geometry, definition      149Ч150
Elliptic geometry, sample three-manifolds      248
Euclidean geometry, definition      149Ч150
Euclidean geometry, list of three-manifolds      248Ч249
Euler number      165Ч185 374
Euler number, definition      174
Euler number, general description      165
Expansion of the universe      260Ч263 265Ч269
Extrinsic property      31Ч35
Flat geometry      120Ч122
Flat surfaces and three-manifolds      99Ч124 273
Flat torus      13Ч20 23Ч24
Flatland      3Ч4 187S
Flatland story, beginning      3Ч9
Flatland story, continuation      45Ч47
Flatland story, ending      65Ч69
Four dimensions      187Ч197
Friedmann      261Ч262 282
Galaxies      260Ч261 289
Galaxies, catalogs of      292Ч293
Gauss      37 208Ч210
Gauss Ч Bonnet formula      165Ч184
Gauss Ч Bonnet formula for elliptic geometry      174
Gauss Ч Bonnet formula for Euclidean geometry      175
Gauss Ч Bonnet formula for hyperbolic geometry      174
Gauss Ч Bonnet formula for surfaces of constant curvature      181
Gauss Ч Bonnet formula for surfaces of varying curvature      182Ч184
Gaussian curvature      181
Geocentric universe      279Ч280
Geodesic      37 136
Geometry      26Ч29
Geometry, Relativity and the Fourth Dimension      190Ч192 195Ч197
Girard      137
Global geometry      41
Global property      39Ч41
Global topology      40Ч41
Gluing      13
God      275
Great circle      136Ч137
Great two-sphere      203 207
Half turn manifold      108 249
Half turn manifold, surfaces in      128
Handle      363
Handle in presence of crosscap      372Ч373
Hexagonal three-torus      122Ч123
Hexagonal torus      111Ч120
Hinton      4
Homeomorphic surfaces      362
Homogeneity      41Ч42
Homogeneity of the Universe      263Ч264
Homogeneous geometry      41Ч42 149Ч150
Homogeneous geometry on surfaces      157Ч164
Homogeneous geometry on three-manifolds      219Ч228 243Ч255
Homogeneous three-manifold      96
Hubble      262
Hubble, constant      262 264
Hyperbolic 3-manifolds      219Ч221 249Ч250 273
Hyperbolic 3-manifolds, cosmic crystallography in      291
Hyperbolic geometry      149Ч156 213Ч218
Hyperbolic geometry for "typical" three-manifolds      249Ч250
Hyperbolic geometry for Seifert Ч Weber space      219Ч221
Hyperbolic geometry for surfaces      157Ч164
Hyperbolic geometry, definition      149Ч151
Hyperbolic geometry, Thurston's work      249Ч250 255
Hyperbolic n-gon      170
Hyperbolic paper      151Ч154
Hyperbolic plane      149Ч156
Hyperbolic space      213Ч218 282
Hyperbolic triangle      154Ч156 214Ч216
Hypersphere      201Ч210
Intrinsic point of view      38Ч39
Intrinsic property      31Ч39
Isotropic geometry      244Ч246
Isotropic three-manifold      96
Isotropy of the microwave background      299Ч300
Isotropy of the Universe      263Ч265
Jungle gym in a nonorientable three-manifold      58Ч59
Jungle gym in a three-torus      21Ч22
Jungle gym, twisted Euclidean      251Ч253
Klein      280
Klein bottle      48Ч58
Klein bottle in four-dimensional space      191
Klein bottle, chess on      50 53Ч55
Klein bottle, cosmic crystallography in      290Ч292
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      50Ч54
Klein perforation      371
Knotted sphere      193Ч195
Lachieze-Rey      287
Last scattering surface      301Ч308
Lehoucq      287
Lemaitre      262
Leucippus      279
Light-year      260
Local geometry      40Ч41
Local property      39Ч41
Luminet      287
Lune, double      139Ч141
Manifold      11
Manifold, precise definition      40Ч41
Manifold-with-boundary      42
MAP      see "Microwave anisotropy probe"
Microwave anisotropy probe      307Ч308
Microwave background radiation      297Ч302 307
Milky Way      260
Mirror reversal      45Ч49
Mirror reversal and orientability      58
Moebius bridge      371
Moebius strip      47Ч49 125Ч126
Moebius strip, two-sided      129
Multiconnected space      280
n-gon      169Ч170
Negative curvature      151
Nonhomogeneous      41
Nonorientable manifold      58
Octahedral space      227
One-dimensional manifold      41
One-sided surface      125Ч131
One-sided surface, definition of      125
Open manifold      42Ч44
Ordinary surface      368
Orientable manifold      58
Orientation-reversing path      58
Pair separation histogram      290Ч291
Patchwork quilt      368
Penzias      297
Perforation      367
Planck satellite      307Ч308
plasma      295Ч297
Poincare conjecture      280
Poincare dodecahedral space      220Ч224 248
Poincare dodecahedral space, circles in the sky of      306
Positive curvature      149
PRODUCT      83Ч97
Product, geometrical      86Ч88 91
Product, multiplication      86
Product, three-dimensional      89Ч97
Projective plane      59Ч64
Projective plane, minus a disk      70Ч73
Projective plane, nomenclature      374
Projective three-space      62Ч64 210Ч212 248 282
Puncto      135
Quarter turn manifold      107Ч110 229Ч233 249
Quarter turn manifold, circles in the sky of      306
Quarter turn manifold, cosmic crystallography in      291
Quaternionic manifold      226Ч227
RADIANS      136
Riemann      280
Rubber band with twist      31Ч33
Schwarzschild      280
Sectional curvature      244Ч247
Seifert Ч Weber space      219Ч221 224 249
Seifert Ч 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      254Ч255
Spacetime      195Ч197 272Ч278
Spergel      306
Sphere      135Ч147 199Ч200
Sphere vs. ball      200Ч201
Sphere, knotted      193Ч195
Sphereland      135Ч136
Spherical 3-manifolds      219Ч224 273
Spherical 3-manifolds, cosmic crystallography in      292
Spherical n-gon      169Ч170
Spherical triangle      136
Spherical triangle, area and angles      136Ч144
Spirits      190Ч193
Starkman      306
Superclusters      289Ч293
Surfaces      11
Surfaces, classification of      361Ч375
Surfaces, Classification Theorem      368
Surfaces, nonredundant list of      80
Surfaces, ordinary      368
Surfaces, redundant list of      76
Surfaces, triangulated      367
Telescope      280
Tetrahedral space      226Ч227
Three-manifold, formal definition      40
Three-manifold, informal definition      11
Three-sphere      199Ч210 248 280 282
Three-torus      20Ч24 249
Three-torus as a product      89Ч91
Three-torus, circles in the sky of      302Ч306
Three-torus, how corners fit      224Ч225
Three-torus, introduced to astronomers      280Ч281
Three-torus, oblong      41
Three-torus, view in      103Ч105
Thurston      249 255
Tic-tac-toe on a Klein bottle      50Ч54
Tic-tac-toe on a torus      14Ч17 103
topology      26Ч31
Torus, $S^{1}\times S^{1}$      84Ч85 87
Torus, chess on      17Ч20
Torus, double      374
Torus, drawn as a doughnut surface      9 30
Torus, flat      13Ч20 23Ч24
Torus, flat torus vs. doughnut surface      30Ч31 41
Torus, hexagonal      111Ч120
Torus, three-dimensional      see "Threetorus"
Torus, tic-tac-toe on      14Ч17 103
Torus, triple      374
Torus, twisted      239Ч241 252Ч253
Triangle, Euclidean      144
Triangle, hyperbolic      154Ч156 214Ч216
Triangle, spherical      136Ч144
Triangulated surface      367
Triple cross surface      375
Triple torus      374
Twisted $H^{2}\times E$ geometry      254
Twisted $S^{2}\times E$ geometry      254
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