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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
Completeness of hyperbolic space      19.2.6
Complex affine spaces      2.8.7
Complex analysis      8.2.14
Complex conjugation      2.6.1
Complex exponential      8.3.7
complex numbers      0.2
Complex numbers and plane similarities      8.8.4 9.6.4
Complex projective quadric C(4)      20.5.7
Complex projective spaces      9.1.7 19.1.5
Complex proper quadrics      14.3.5
Complex structure for Euclidean plane      8.3.12
Complexification      5.0.5 7 7.4.1 18.6.13.11
Complexification of a projective morphism      7.5.4
Complexification of a projective space      7.5.1
Complexification of a real vector space      7.1.1
Complexification of an affine morphism      7.6.3
Complexification of an affine space      7.6.2
Complexification of conics      17.4.1
Complexification of morphisms      7.2
Complexification of polynomials      7.3
Complexification, canonical      7.0.5
Complexification, natural      7.7.5
Complexifications and similarities      8.8.6
Complexifications and subspaces      7.4
Computation      see “Calculation”
Concave function      11.8.6
Concavity      9.14.18
Cone      11.1.6 11.6.2 14.5.3
Conformal chart      18.1.7.2
Conformal group      20.6.1
Conformal map      9.5.4.2 18.10.3.1 19.8.6
Conformal model      19.6.1
Congruent      10.2.6
conic      1.2.7 1.4.2 13.3.2 14.1.1 15.1.1
Conic at infinity      15.1.3.2
Conjugate diameters      15.5.10
Conjugate elements in $S_{n}$      1.6.4
Conjugate of a quaternion      8.9.1
Conjugate set      15.6.3
Conjugate subgroup      1.5.3
Conjugation      2.6.1
Conjugation by inversions      10.8.4
Conjugation with respect to a quadric      14.5.1
Conjugation, complex      7.1.1 7.5.1 7.6.2
Connectedness of $O^{+}(E)$      8.4.3
Connectedness of the complement of subspaces      2.8.7
Connectedness of the projective group      4.9.5
Connectedness of the sphere      18.2.1
Conoid      14.1.7.1
Constant vector field      3.1.2.1
Constant width      12.10.5
Contact theory      16.4.11.3
Continuous screw motion      9.14.7
Convex compact sets      9.4.3
Convex cone      11.1.6
Convex curve      11.3.10.1
Convex function      11.8 11.5.1 11.8.10 11.8.12 11.9.15
Convex hull      11.1.8.1
Convex polar body      see “Polar body”
Convex polyhedron      12.1.1
Convex sets      8.2.5.3 11 11.1.1 11.4 12.9.1
Convex sets, frontier of      11.6
Convex sets, topology of      11.3
Convex spherical polygon      18.7.1
Convex surface      11.3.10.2
Convexity criteria      11.1.7 11.8.11
Convexity inequalities      11.8.11.12
Convexity of quadrics      15.4.6
Coordinates, affine      2.2.9
Correlation      14.5.5 14.8.12.1
Cosine      8.3.6
Cosine-haversine formula      18.6.11
Cosiuus      18.11.24
Cowlick      18.2.5.4
Cramer’s Rule      6.2.1
Crank      10.8.3
Cross product      8.11 8.11.8 8.12.9 15.6.6
Cross-ratio      6.1.2 6.8.13 9.6.5 10.13.17 14.4.4 16.2.5 16.2.7.3
Cross-ratios and duality      6.5
Cross-ratios and field structure      6.4.8
Cross-ratios and projective coordinates      6.5.10
Cross-ratios, action of permutations on      6.3
Cross-ratios, calculation of      6.2
Crystal      12.5.5.7
Crystallographic groups      1.7 1.7.3 1.9.9
cube      1.8.3.4 12.1.2.5 12.5.4.2
Cubic      16.6.1
Cultural constructs      12.5.5.7
Cup product      II.86
Curvature      9.10.7 12.10.9.1 17.7.4 17.9.9 18.3.8.6
Curvature, lines of      9.5.4.21
Curve      2.8.12 9.9.1
Curves of constant width      12.10.5
Cycles of a permutation      1.6.4
Cyclic group      0.2
Cyclic permutation      10.4.5.1
Cyclic points      9.5.5.1 10.13.1.3 17.4.1 17.4.3 17.5
Cyclid      20.7.2
Cylindrical wedge      12.12.20.5
D.K. Kazarinoff      10.4.6
da Vinci, Leonardo      I.26 II.3
Dandelin      17.3
Darboux, theorem of      20.8.7
De Divina Proportione      I.26 II.3
Deficit      12.11.9.3
Degenerate conic      16.4.10
Degenerate Quadratic Form      13.2.1
Degenerate quadric      14.1.1 14.2.7.5 14.5.6
Degenerate simplex      14.5.4.1
Degree      18.2.5.2
Derivative      2.7.7
Desargues      4.0.2 5.0.1
Desargues’s theorem      2.5.4 2.6.7 4.8.3 5.4.3 5.4.7 6.7.4 14.2.8.3 16.5.4
Descartes      17.1.6
Descartes oval      9.14.22
Descartes’s law      9.14.22
Descartes’s principle      17.1
Determinant of a form      11.8.9.2
Diagonalization      see “Orthogonalization”
Diameter and Steiner symmetrization      9.13.4
Diameter of a quadric      15.5.7
Diameter of a set      0.3
DICTIONARY      14
Dido      12.11.7
Dieudonne      13
Difference set      0.1
Differentiability of convex functions      11.9.16
Differentiable calculus      2.7.7
Differentiable curve      2.8.12
Differentiable equation      6.6.7 6.8.12
Differentiable forms      18.3.4
Differentiable geometry      4.0.5 6.6 9.10 9.5.4.1 9.5.4.9 10.8.5 13 16.4.12 18.10.3 19.6.12 19.7.3
Differentiable hypersurface      11.9.23
Differentiable manifold      1.7.7.4 4.2.6 4.3.2 9.10.7 9.12.2 9.12.7 9.9.6 10.7.4 11.3.10.1 11.9.23 12.10.9.1 14.8.5 18.10.3.1 18.3.1 19.1.1.4
Differentiable manifolds of constant negative curvature      12.6.8
Differentiable maps, singularities of      12.6.8
Differentiable operators      13.5.6
Difficulty in measuring angles      8.3.13
Dihedral angle      12.1.12
Dihedral group      0.2 1.8.3.4 1.8.7 12.4.5
Dilatation      2.3.3.12 6.6.2
Dilatations, characterization of      2.5.6 5.2.1
Dimension of a convex set      11.2.6
Dimension of a projective space      4.1.1
Dimension of A(X;X')      2.3.4 2.3.9
Dimension of an affine space      2.1.8
Dimension of an affine subspace      2.4.1
Dinghas — Hadwiger — Bonnesen inequality      12.11.9.3
Diopters      9.14.22
Direct sum      0.2
Direction of a line      19.2.10
Direction of an affine subspace      2.4.1
Directrix      17.2.1.4 11.9.1
Discrete action      1.7.5.1
Discriminant      13.1.4.6
Distance      0.3
Distance function      11.8.12.2
Distances in Euclidean affine spaces      9.2.2 9.2.5 9.7 9.10
Distinguished point      3.1
Division algebras      12.6.8
Division by zero, convention about      6.2.2
dodecahedron      1.8.3.4 1.8.4 12.5.5
Domestic animals      10
Dominated Convergence Theorem      0.6
Doors      8.1.8.5
Double pedal      9.6.8
Double point      4.5.18 14.1.5.3
Dowker’s theorems      12.12.5
Dual poly tope      12.6.2.4
Dual, algebraic      0.2
Duality      6.5 8.1.8 11.1.5 12.1.2.6 16.5.6
Duality with respect to a quadric      14.5
Dupin eyelid      18.11.19 20.7.3
Dupin’s theorem      9.5.4.21
Dvoretsky      11.7.5
Eadem mutata resurgo      9.6.9
Earth      4.7.5 18.1.3.2 18.2.5.4
Eccentric spheres      10.7.5
Eccentricity      17.2.1.4 17.9.23
EDGE      10.6.1
Edge of a polyhedron      12.1.8
Edge of a triangle      2.4.7
Egyptian tablet      10.6
Eiffel Tower      II.146
Eigenvectors of quadratic forms      13.5.1
Elation      16.4.13
electricity      9.14.34.6
Elegance      7.0.3
Element of volume      18.3.7.1
Elementary geometry      4
Elementary volume      12.2.6
Elements      2.6.7
Eleven-point conic      16.5.5.1
Elie Cartan      8.10.3
ellipse      1.4.2 9.4.3 12.12.12 15.8.8.2 17.7
Ellipsoid      12.12.2 15.3.3.3 15.6.3 15.7.9
Ellipsoid of inertia      13.5.6
Ellipsoid of revolution      18.1.5.3
Ellipsoid, volume of      11.8.9.1
Elliptic equilateral sets      19.8.24
Elliptic function      16.6.1
Elliptic geometry      19.1
Elliptic integral      17.7.5
Elliptic paraboloid      15.3.3.3
Elliptic space      9.7.4 19.1.1.1
Elliptic transformation      6.8.8
Endomorphism      2.4.9.7
Endpoint of a curve      9.9.1
Endpoint of a half-line      19.1.1.5
Endpoint of a segment      3.4.3
Envelope      9.6.7 11.8.12.5 17.8.3.2
Envelope equation      14.6.1 14.8.13
Epicycloid      9.14.34.1 12.12.20.1
Epigraph      11.8.3
Equality of triangles      10.2.6 18.6.13.10 18.11.8 19.8.4
Equation of a quadric      14.1.1 15.1.1
Equations of the center      15.2.4
Equator      18.1.2.3
Equiaffine curvature      2.8.12
Equiaffine geometry      2.7.6
Equiaffine length      2.8.12
Equibarycenter      8.4.2
Equidistant hyperplane      9.7.5.1 19.4.2
Equidistant loci      18.4.6 19.1.2.3
Equilateral hyperbola      17.1.8 17.5.1 17.8.3 17.9.16
Equilateral set      19.8.24
Equilateral triangle      10.1.8 18.6.18.9
Equivalence of quadratic forms      13.1.4
Equivalent chart      18.1.7.4
Erdoes — Mordell, theorem of      10.4.6
Ergodic theory      9.4.4 19.7.3
Erlangen program      1
Escher, M.C.      4.7.6 1.7.4 1.7.6 1.7.7.6 19.6.12
Essential singularity      9.5.4.8
Etruscans      12.5.5.7
Euclidean affine plane      see “Euclidean plane”
Euclidean affine quadrics      15.6
Euclidean affine space      see “Euclidean space”
Euclidean geometry      1.8.6 8.1.8.5
Euclidean plane      3.4.2
Euclidean plane, complex structure for      8.3.12
Euclidean plane, tilings of      1.7.4 12.6.10.4
Euclidean space      2.7.5.8 3.7.8 7.0.1 9.1.1
Euclidean terminology      8.4.7.3
Euclidean vector space      1.2.5 8.1.1
Euclid’s axioms      2.4.4
Euclid’s definitions      2.4.9.1
Euclid’s Elements      2.6.7
Euclid’s fifth postulate      2.4.9.5 II.319 19.1.1.6
Euler angles      8.9.5
Euler characteristic      12.7.5.4 12.10.9.2
Euler equation      11.8.12.5 12.12.15
Euler formula      12.7.3
Euler identity      8.7.12
Everyday experience      2.7
Evolute      9.10.8 9.14.21 9.14.34.4 17.7.4
Exact homotopy sequence      8.10.3
Excellent space      9.9.4.4
Exponential map      8.3.7
Exposed point      11.6.4
Extended real line      5.2.3
Exterior algebra      4.3.3.1 8.11.1
Exterior bisector      9.4.1 10.1.4
Externally tangent      10.7.5
Extremal point      11.6.4 11.9.8 12.1.9
Eyesight      4.0.4 4.7.3
Face of a polyhedron      12.1.5
Face of a triangle      2.4.7
Faithful action      1.3.1
Fedala, Spain      II.132
Fedorov      1.7.7.1
Fermat      9.10.6
Fermat numbers      12.4.6
Fermat’s problem      10.4.3
Feuerbach theorem      10.11.3
Fiber      18.1.3.6
Fiber bundle      8.10.3
Field automorphism      2.6.1 14.8.12.2
Field of prime characteristic      3.7.1
Field structure and cross-ratios      6.4.8
Field with four elements      6.3.2
Field with seven elements      16.8.17
Field with three elements      16.8.16
Fields, convention about      0.2
Finite fields      4.1.3.7 4.6.16 4.9.11 12.6.8 13.1.4.5
Finite geometry      15.4.8
Finite subgroups of $Is(S^{d})$      18.5.10
Finite subgroups of GA(X)      3.7.3
Finite-dimensional affine spaces      2.7
Finiteness of stabilizers      9.8.5
First fundamental theorem of projective geometry      4.5.10
First variation formula      9.4.1.2 9.10.1 9.10.7
Fixed points of homographies      6.6.1
Flag      12.5.1
Flat angle      8.7.3.1
Flat torus      18.11.17
Flexible      12.8.2
Focal axis      17.2.1.4
Focal circle      17.9.1
Focal point      6.6.4
1 2 3 4 5 6
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