Berger M., Pansu P., Berry J.-P. — Problems in Geometry :: Электронная библиотека попечительского совета мехмата МГУ

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Berger M., Pansu P., Berry J.-P. — Problems in Geometry

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Название: Problems in Geometry

Авторы: Berger M., Pansu P., Berry J.-P.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1984

Количество страниц: 266

Добавлена в каталог: 09.07.2005

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Предметный указатель

Action (of a group on a set)      1.A
Affine conies      16.1
Affine form      2.B
Affine frame      2.E
Affine group      2.A
Affine map      2.B
Affine quadratic form      1S.A
Affine reflection      2.D
Affine similarity      9.D
Affine subspace      2.D
Angle between lines      8.F
Angle of a rotation      8.D 9.E
Anisotropic form      13.C 13.1
Appolonius’ formula      9.F
Appolonius’ Theorem      12.4 (sol) 15.D 17.P
Archimedes’ method      15.1
Area (of a convex compact set)      12.B
Artin space      13.2
Barycenter      3.A
Barycentric coordinates      3.0
Barycentric subdivision      3.A
Bezout’s Theorem      16.E
bisector      8.F
Blaschke rolling Theorems      12.S
Boundary points of a convex      11.C
Brianchon, theorem of      5.3 (sol) 16.C
Cartan — Dieudonne, Theorem of      13.E
Center of a similarity      9.D
Central angle      10.D
Central quadric      15.C
Centroid      2.G 3.A
Ceva’s theorem      2.1
Class formula      1.E
Classification of quadratic forms      13.B
Classification of quadrics      14.C
Clifford parallelism      18.D
Cocube      12.C
Compass, constructions with      10.6
Complementary subspace      2.D
Complete quadrilateral      6.B 16.4
Complex homographies      6.6
Complexification      7.A 7.B 7.C
Conformal group      18.E
conic      14.A 15.A
Conjugate diameters      15.C
Conjugation (in a complex space)      7.A
Conjugation (with respect to a quadric)      14.E
Convex hull      11.A
Convex set      11.A
Cross-ratio      6.A
Cross-ratio (on a conic)      16.C 16.3
Crystallographic groups      1.G
cube      1.F 12.C
Cyclical points      7.D 9.D 17.C
Darboux’s theorem      20.3
Degeneracy      13.C
Degenerate form      13.C
Degenerate quadric      14.A
Degree (of a vertex)      1.H
Desargues’s theorem      16.F
Diameter of a quadric      15.C
Dihedral group      12.C
Dilatation      2.C
Dimension (of a convex set)      11.A
Dimension (of a projective space)      4.A
Direct similarity      8.G
Direction (of an affine subspace)      2.D
dodecahedron      1.F 12.C
Duality (in projective spaces)      6.C
Dupin eyelids      18.7 20.2
ellipse      1S.B
Ellipsoid      1S.B
Elliptic geometry      19.A
Envelope equation      14.F
Equation of a quadric      14.A
Equiaffine curvature      2.4
Equiaffine length      2.4
Equilateral hyperbola      17.A
Equilateral sets      19.1
Equivalence of quadratic forms      13.B
Erlangen program      1.C
Euclidean affine spaces      9.A
Euclidean conies      17. A
Euclidean vector space      8.A
Euler’s identity      3.6
Excellent metric      9.G
Excentricity      17.B
Extremal points      11.C
Finite fields      4.5 13.2 13.4 16.7
First variation formula      9.G
Foci of a conic      17.B
Folding      12.1
Ford circles      10.8
Fundamental domain (of a tiling)      1.2 19.4
Fundamental theorem of affine geometry      2.F
Fundamental theorems of projective geometry      4.E
Geometry      1.C
Girard’s formula      18.C
Good parametrization      16.B
Gram determinant      8.J
Grassmann manifold      14.1
Great circle      18.A
Great Theorem of Poncelet      16.H 16.5
Group of a quadratic      14.G
Group of a quadratic form      13.E
Group of a regular polytope      12.C 12.2
Guldin’s Theorems      12.3
Habn-Banach Theorem      11.B
Half-space      2.G
Harmonic conjugates      6.B
Harmonic division      6.B
Harmonically circumscribed quadric      14.E
Harmonically inscribed quadric      14.3
Helly’s theorem      11.B
Hexagonal web      5.3
Hilbert geometry      11.3
Homofocal quadrics      15.6
Homogeneous coordinates      4.C
Homogeneous space      1.B
Homographies, eigenvalues of      6.5
Homography      4.E 6.D
Homography (of a conic)      16.D
Homography axis      16.D
Homokinetic joints      18.6
Homothety      2.C
Hooke joints      18.6
Hyperbola      15.B
Hyperbolic geometry      19.B
Hyperbolic trigonometry      19. C
Hyperboloid      15.B
Hyperplane at infinity      5.A
Hyperplane of support      11.B
icosahedron      1.F 12.C
Image of a quadric      14.A
Inscribed angle in a circle      10.D
Intrinsic metric on a sphere      18.A
Invariance subgroup (of a tiling)      1.H
Inverse similarity      8.G
Inversion with respect to a sphere      10.C
Involution      6.D
Irreducible groups      8.1
Isodiametric inequality      9.H
Isogonal tilings      1.H
Isohedral tilings      1.H
Isometry (in a Euclidean vector space)      8.A
Isotropic cone      8.H 13.C
Isotropic lines      8.H
Isotropic vectors      13.C
Isotropy subgroup      1.D
Klein model      19.B

Klein, Felix      1.C
Krein and Milman’s Theorem      11.C
Laguerre formula      8.H 17.C
Latitude      18. A
Lattice      1.G
Lebesgue measure      2.G 9.H
Length of a curve      9.G
Light polygon      9.3
Limacon      9.6
Limit points of a pair of circles      10.D
Line of the images      10.3
Linear independence (in affine spaces)      2.E
longitude      18. A
Loxodromes      181
Lucas’s theorem      11.4
Marked tilings      1.H
Mass      3.A
Measure (in affine spaces)      2.G
Menelaus’ theorem      2.1
midpoint      2.A
Miguel, Theorem of six circles of      10.D 10.6
Mixed product      8.J
Moebius group      18.E
Moebius tetrahedra      4.6
Mohr — Mascheroni, Theorem of      10.6
Morphism (between projective spaces)      4.E
Motions      9.A
Napoleon — Mascheroni, problem of      10.6
Non-singular completion      13.E
Null subspace      13.C
Operation (of a group on a set)      1.A
Orbits      1.E
Orientability of real projective spaces      4.2 4.3
Orientation (of a Euclidean vector space)      8.J
Orientation (of an affine space)      2.G
Oriented angle between lines      8.F
orthocenter      10.1
Orthogonal group      8.A
Orthogonal reflection      8.C
Orthogonal sets      8.B
Orthogonal symmetry      8.C
Orthogonal vectors      8.A
Orthogonality      13.D
Orthonormal set      8.A
Osculating conies      16.E
Pappus, theorem of      5.D 5.3
parabola      15.B
Paraboloid      15.B
Pascal limacon      9.6
Pascal’s theorem      16.2
Pencil of hyperplanes      4.B
Pencil of lines      4.B
Pencils of conies      16.F
Pencils of quadrics      14.D
Permutation group      1.A
Perspective      4.F 11.3
Plane tilings      1.G
Poincare model      19.D
Point at infinity (on a projective line)      5.A
Polar form      13.A
Polar hyperplane      14.E
Polar reciprocal      11.B
Polarity with respect to a quadric      14.E 15.C
Polarity with respect to a sphere      10.B
Pole of a hyperplane      14.E
Pole of an inversion      10.C
Poly spheric coordinates      20. C
POLYGONS      12.A
Polynomials (in an affine space)      3.E 3.4 3.5
Polytopes      12.A
Poncelet, Great Theorem of      16.H 16.5
Power of a point with respect to a sphere      10.B
Problem of Napoleon — Mascheroni      10.6
Projective base      4.D
Projective completion      5.A
Projective conies      16.A
Projective group      4.E
Projective independence      4.B
Projective quadric      14.A
Projective space      4.A
Proper quadric      14.A
Pull-back      13.A
Quadratic form      13.A
Quadric      14.A
Quaternions      8.1 8.5
Radical      13.C
Rank of a quadratic form      13.C
Rank of a quadric      14.A
Reflection (orthogonal)      8.C
Reflection around Y and parallel to Z      2.D
Regular pentagon      12.1
Regular polyhedra      1.F
Regular polytope      12.C
Regular simplex      12.C
Rhumb lines      18.1
Ricatti equation      6.2
Robinson non-periodic tiling      1.4
Rotation      8.A
Ruler and compass, constructions with      5.2 10.6
Scalar product      8.A
Screw motion      9.C
Segment      3.C 9.G
Self-polar simplex      14.E
Semi-affine map      2.F
Semi-linear map      2.F
Similar triangles      10.A
Similarity      8.G
Simple connectivity      18.A
simplex      2.E
Simply transitive operation      1.D
Singular subspace      13.C
Space of spheres      20.A
Special affine group      2.B
Spheres      10.B
Spherical geometry      18.A
Spherical triangles      18.C
Spherical trigonometry      18.C
Spherometer      18.1
Stabilizer      1.D
Star-shaped      11.A
Steiner symmetrization      9.H
Stereographic projection      18.A
Strict triangle inequality      9.A
Superosculating conies      16.E
Sylvester’s law of inertia      13.B
Sylvester’s theorem      9.1
Symbol of a form      15.A
Symmetric group      1.A
Symmetry (orthogonal)      8.C
Symmetry around Y and parallel to Z      2.D
Tangential conies      16.G
Tangential pencils      14.F
Tangential quadric      14.F
Theorem of Brianchon      5.3 (sol) 16.C
Theorem of Ceva      2.1
Theorem of Desargues      5.D
Theorem of Menelaus      2.1
Theorem of Mohr — Mascheroni      10.6
Theorem of Pappus      5.D 5.3
Theorem of six circles of Miguel      10.D 10.6
Topology (of a projective space)      4.G
Torus of revolution      18.D 20.2
Transitive operation      1.B
Translation      2.B
Triangles      10.A
Umbilical      9.D
Universal space      3.D
Upper half-space model      19.D
Valency      1.H
Vector product      8.J 8.6

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