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Berger M., Cole M. (translator) — Geometry I (Universitext)
Berger M., Cole M. (translator) — Geometry I (Universitext)



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Название: Geometry I (Universitext)

Авторы: Berger M., Cole M. (translator)

Аннотация:

This is the first part of the 2-volume textbook Geometry which provides a very readable and lively presentation of large parts of geometry in the classical sense.
An attractive characteristic of the book is that it appeals systematically to the reader's intuition and vision, and illustrates the mathematical text with many figures. For each topic the author presents a theorem that is esthetically pleasing and easily stated - although the proof of the same theorem may be quite hard and concealed. Many open problems and references to modern literature are given. Yet another strong trait of the book is that it provides a comprehensive and unified reference source for the field of geometry in the full breadth of its subfields and ramifications.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Corrected Fourth Printing

Год издания: 2009

Количество страниц: 427

Добавлена в каталог: 14.04.2010

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Предметный указатель
Foci, determination of      17.9.24
Focus      17.2.1.4 17.4.3 18.11.15
Ford circle      10.13.29
Forms and densities      9.12.2
Formula of the median      9.7.6.5 9.8.6.4
Formula of the three levels      12.12.20.7
Formulas for hyperbolic space      19.6.9
Formulas for spherical triangles      18.6.13
Formulas for triangles      10.3
Foundry      II.152
Four-sphere      4.8.2 18.1.3.4
Fourier series      12.11.9.4 12.12.12
Fractal      9.9.3.3
Frame      see “Affine frame”
Free fall      17.5.5.5
Free vector      2.1.3
Fregier point      16.3.6 16.8.7
Fregier’s theorem      16.3.6
Frontier of a convex set      11.6
Frustum      10.6.8.1
Fubini-Study metric      19.8.22
Fubini’s Theorem      0.6 9.12.3 11.3.2 12.11.4
Fuchsian group      19.6.12
Full pencil      16.5.1
Functional analysis      11.4.2
Functorial correspondence      3.2.2
Functoriality      5.1.3
Functoriality of complexification      7.2
Fundamental domains      1.9.12
Fundamental formula of hyperbolic trigonometry      19.3
Fundamental formula of spherical trigonometry      18.6.8
Fundamental group      8.10.3 12.7.5.3 18.2.1
Fundamental quadratic form      20.2.1
Fundamental quadric      20.2.4
Fundamental theorem of affine geometry      6.4.8 2.6.3
Fundamental theorem of projective geometry, First      4.5.10
Fundamental theorem of projective geometry, Second      5.4.8
Fundamental tiling      1.7.4
G-action      1.1.1
GA(X), compact subgroups of      2.7.5
GA(X), finite subgroups of      3.7.3
Galois theory      12.6.10.3
Game theory      11.8.10.10
Gauge      11.8.12.1
Gauss      12.4.6 18.1.5.3
Gauss approximation      6.6.5
Gauss projection      18.1.8.3
Gauss — Bonnet formula      18.3.8.6
Gauss — Bonnet theorem      12.7.5.2
Gauss’s method      13.4.8
General topology      0.4
Generalized circle      17.4.2.1
Generalized sphere      20.1 20.5.1
Generating lines      13.7.10 14.4.1
Generators for O(E) and $O^{+}$      8.4
Genus      12.7.5.4
Geodesic      9.9.6
Geodetic reference spheroid      18.1.5.3
geoid      18.1.5.3 18.1.6.3
Geometric algebra      8.5 13.3.5
Geometric arcs      9.9.2
Geometric constructions      6.2.7 6.4.6 9.3.6 9.6.2 12.4.6
Geometric realization of hyperplane reflections      14.7.4
Geometrical optics      6.6.5 6.8.4
Geometry      1.4 13.7.2
Geometry of numbers      11.9.16
Gerardin      14.8.16
Gergonne      10.11.1
Germany      II.133 II.152
Ghost edges      12.8.6.4
Girard’s formula      18.3.8.4
GL(E), compact subgroups of      11.8.10.8
Good conic      16.5.4
Good parametrization      16.2.9 16.7.2
GP(E), involution in      4.5.19 6.4.7
GP(E), topology of      4.5.20
Gram determinant      8.11.5 9.2.6.2 9.7.3.3 15.6.3 18.11.13 18.3.7.1
Gram — Schmidt orthonormalization      8.1.4
Grassmannian      1.2.5 1.5.9 1.9.10 8.2.7 8.6.1 14.3.7 14.8.4
Grassmannian coordinates      2.4.8.8
Graves      17.6.4
Great circle      18.1.2.1
Greeks      2.7 I.152 I.200 12.5.5.7 II.170
Greenwich meridian      18.1.6.5 18.1.8.3
Gromov      12.11.4
Ground field      see “Base field”
Group action      1.1.1
Group action, discrete      1.7.5.1
Group action, faithful      1.3
Group action, p-transitive      1.4.5
Group action, section of a      1.6.6
Group action, simply transitive      1.4.3
Group action, transitive      1.4
Group actions associated with a great circle      18.8.3
Group of a proper quadric      14.7
Group of a quadratic form      13.6
Group of permutations      0.2
Group presentations      1.8.7
Group structure on spheres      8.9.1
Guldin, theorems of      12.12.20.9
Haags Gemeentemuseum, The Hague      1.7.4 1.7.6 4.7.6 19.6.12
Haar measure      8.2.5.1
hadamard      7.0.1
Hahn — Banach theorem      11.4.1
Hairy ball      12.11.5 18.2.5.4
Half-line      8.6.1
Half-lines in elliptic space      19.1.1.5
Half-lines in hyperbolic space      19.2.10
Half-perimeter      10.3
Half-space      2.7.3
Half-space model      19.7.1
Halving angles      8.7.3 8.7.7.7
Harmonic conjugate      6.4.5
Harmonic division      6.4.1 10.7.10.2 16.2.5 19.4.2
harmonic oscillator      13.5.6
Harmonic quadrilateral      9.6.5.2 9.14.15
Harmonically circumscribed      14.5.4.4 14.8.6 17.9.5
Harmonically inscribed      14.8.10
Hart      16.6.1
Hausdorff distance      9.11.1 9.12.5 12.9.1
Hausdorff metric      9.11
Hausdorffness of projective spaces      4.3.3
Haversine      18.6.11
Heaven and Hell      II.342
Helix      10.12.3 10.13.22 18.9.3
Helly’s theorem      11.7.4.2 11.7.7 11.9.18
hemisphere      18.7.1
Heredity      10.8.1.1 14.1.3.3 14.5.2.4
Hermitian space      13.5.7
Heron’s formula      10.3.3 10.13.7
Hersch’s theorem      18.10.9
Heuristic remark      4.3.8 12.6.8
Hexagonal web      5.5.8 5.5.9
hilbert      19.7.2
Hilbert geometry      11.9.4
Hilbert spaces      13.5.6 II.86
Hilbert — Dehn problem      12.2.7
Historical models      19.7.2
Historical remarks      1.7.7.1 4.0 10.9.2.1 13.3.2 II.116 II.170 II.318 19.1.1.6
Hoelder inequalities      11.8.11.8 12.11.5.4
hole      12.7.5.4
Holomorphic function      9.5.4.3 18.1.3.2
Homofocal conics      17.6.3.1
Homofocal quadrics      15.7.17
Homogeneity of affine spaces      2.2.3
Homogeneous coordinates      14.1.4.1 6.2.1 7.5.5 4.2.3 4.4.3 4.5.13
Homogeneous of degree k      3.3.2.1 3.7.12
Homogeneous piece of wire      2.7.5.6
Homogeneous plate      2.7.5.3 3.4.2
Homogeneous polynomial      3.3.1
Homogeneous space      1.5.4
Homogenizing variable      3.3.13
Homographies of a conic      16.3.1
Homographies of a projective line      6.6 6.8.15
Homographies, fixed points of      6.6.1
Homography      4.5.2 4.5.16 4.7.3 6.4.11 16.2.3 16.4.13
Homography axis      16.3.3
Homography, invariants of      6.1.7
Homokinetic joint      18.11.16 18.11.16
Homology groups      18.2.5.1
Homomorphisms, set of      0.2
Homothety      6.6.2 8.8.3 2.3.3.9 3.1.2.2
Homotopic bases      2.7.2.7
Hooke joint      18.11.16 18.11.16
Hopf fibration      1.2.9 1.6.4 4.3.7 18.1.3.6 18.9.4.2 18.11.30
Horocycle      19.6.8.3
Horosphere      19.8.15
Horror cycle      19.6.8.3
Hyperbola      13.8.4 15.3.3.2 17.8
Hyperbolas, specific properties of      17.8
Hyperbolic cosine      13.8.9 0.5
Hyperbolic distance      13.8.7
Hyperbolic geometry      13.8.4 1.8.6 18.3.8.6
Hyperbolic paraboloid      15.3.3.3
Hyperbolic plane      13.8.4 13.1.4.4
Hyperbolic regular polyhedron      19.8.26
Hyperbolic sine      0.5
Hyperbolic space      9.1.7 9.7.4 19
Hyperbolic tangent      0.5
Hyperbolic tiling      19.6.12
Hyperbolic transformation      6.8.8
Hyperbolic triangle      19.8.25
Hyperbolic trigonometry      19.3
Hyperboloid      15.3.3.3
Hyperplane      2.4.2.1 2.7.3
Hyperplane at infinity      5.1.3
Hyperplane reflection      9.2.4 13.6.6.1 14.7.4 19.4.2
Hyperplanes as spheres      20.3.5
Hyperplanes in hyperbolic space      19.2.10
Hypocycloid      9.14.34.1 10.4.5.5 10.11.3 12.12.20.1 17.8.3.2
icosahedron      1.8.4 8.12.12 12.5.5
Icosahedron group      12.5.5.6
identity map      0.1
Identity matrix      0.2
Image focal point      6.6.4
Image measure      0.6
Image of a quadric      14.1.3.8 15.1.1 15.1.3.2
Images, line of the      10.13.16
Imaginary radius      20.1.8
Improper motions      9.1.4
Incommensurable rotations      8.4.7.3
Independent set      2.4.8
INDEX      13.7.5 14.1.1
Inequalities      10.4 12.11.9
Infinitesimal angles      9.5.4.1
infinity      4.5.15
Infinity, conic at      15.1.3.2
Infinity, hyperplane at      5.1.3
Infinity, point at      4.0.2 5.2.3 5.3 10.7.11 15.1.3.2 20.1.8
Infinity, quadric at      15.1.8.2
Infinity, sending objects to      5.4
Inner automorphism      1.2.6 1.3.1 1.4.2 1.5.2 1.6.7.2 2.7.5.11 6.8.13 8.10.2
Inscribed polygon      9.4.2
Inscribed triangle      9.4.1 10.1.5
Institut Geographique National      18.1.8.5
Integers      0.2
Integral geometry      12.11.9.5
Integration theory      18.3.1 0.6
Interior      19.1.3.3
Interior bisector      10.1.4
Interior radius      11.9.12
Internally tangent      10.7.5
International Date Line      18.1.6.1
Intersection of affine subspaces      2.4.9
Intersection of projective subspaces      4.6.10
Intersection of subspaces      4.0.1
Intersection of two conics      16.4
Intersection of two spheres      10.7.5 20.4
Intrinsic metric      9.9.7 9.9.8 9.14.30 18.4.2
Intrinsic space      9.9.4.4
Invariance of domains      9.5.4.2 18.2.6.5
Invariants of homography      6.1.7
inversion      9.5.3.6 9.5.4.4 9.5.4.18 9.14.15 10.8 18.9.1 18.10.1.4 19.6.11
Inversion and osculating circles      10.8.5.5
Inversion of a sphere      18.10.3.2
Inversion preserve angles      10.8.5.2
Inversion sphere      10.8.1.1
Inversions and differential geometry      10.8.5
Involution      6.7.1
Involutions of a conic      16.3.1
Involutions of GP(E)      4.5.19 6.4.7
Involutions of O(q)      13.6.6
Involutive      14.8.12.2
Involutive correlations      14.5.5
Irreducible linear map      8.2.6
Is(X), generators of      9.3
Islam      1.7.1
Isogonal circles      10.13.20
Isogonal spheres      20.4.4
Isolated point      1.7.5.1
Isometric chart      18.1.7.1 18.11.2
Isometric charts, non-existence of      18.4.4
Isometric spaces      13.1.4.1
Isometries of Artinian planes      13.8
Isometries of elliptic spaces      19.1.2.2
Isometries of Euclidean affine spaces      9.1 9.3
Isometries of hyperbolic space      19.4
Isometries of the sphere      18.5
Isometry      8.1.5 0.3
Isometry group      1.2.8
Isomorphic spaces      13.1.4.1
Isomorphism between affine spaces      2.2.6
Isomorphism, set of      0.2
Isoperiinetric inequality      10.4.1 10.5.1 12.12.16 12.11
Isosceles      10.1.3 10.2.2
Isotropic      13.2.1
Isotropic cone      8.8 8.8.6.1 13.2.1
Isotropic lines      8.8 8.8.6.1 13.2.3.1 14.4.7
Isotropy group      9.8.1 1.5.1
Italy      II.22
Iterates of a homography      6.8.5
Jacobi identity      8.12.9
Jacobian      4.9.4
Joachimstal’s theorem      17.9.10
Jordan curve theorem      18.2.6.3
Jordan decomposition      4.5.16
Jordan — Brouwer separation theorem      18.2.6
Jung’s theorem      11.5.8 11.9.18
k-face of a polyhedron      12.1.8
Kakutani’s lemma      11.9.19
Kirchberger’s theorem      11.9.10
Klein bottle      1.7.7.4
Klein group      0.2 6.3.2
Klein model      19.2.5
Klein, Felix      1.4
Krasnosel’skii’s theorem      11.7.7
Krein — Milman theorem      11.6.8
Kritikos theorem      11.9.23
Kugelungsatz      12.11.2 12.11.5.3
Laguerre      20.6.4
Laguerre formula      8.8.7.2 17.4.3.1
Laguerre’s circles      10.11.6
Lahire theorem      17.9.14
Lahire’s cogwheel      9.14.34.3
Lambert projection      18.1.8.5 18.11.27
Latin quotation      9.6.9
Latitude      18.1.6.1
Latitude-longitude chart      18.1.6.1 18.3.4
Lattice      1.7.5.2 9.14.29
Least-perimeter polygon      9.14.10
1 2 3 4 5 6
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