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