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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
$Is(S^{d})$, finite subgroups of      18.5.10
$L_{p}$-spaces      11.8.11.12
$O^{+}(3)$      1.8.1 4.3.9.2
$O^{+}(E)$, connectedness of      8.4.3
Abelian group      1.4.4.1 8.3.3
Accumulation point      9.11.4
Acerbas      12.11.7
action      see “Group action”
Action of permutations on cross-ratios      6.3
Acute angle      10.1.8
Acute triangle      9.4.1.3
Adjacent      12.1.12 12.1.8 12.8.6.2
Adjoint of an endomorphism      8.1.8.6 13.2.4
Aerial photography      4.7
Affine automorphism      2.3.1
Affine conic      16.7
Affine coordinates      2.2.9
Affine Euclidean spaces      see “Euclidean affine spaces”
Affine form      2.4.8.3 11.8.7.2
Affine frame      2.2.9 3.2.5 4.4 2.2
Affine frame, convention about      2.2.8
Affine geometry vs. projective geometry      5.4.2
Affine geometry, fundamental theorem of      2.6
Affine geometry, shortcomings of      5.0.1
Affine group      2.3.3.4 1.2.7
Affine independent set      2.4.3
Affine isomorphism      2.3.1
Affine map      see “Affine morphism”
Affine morphism      2.3 2.3.1 3.2 3.5
Affine polynomial      3.3.5
Affine quadratic form      3.3.6 15.2
Affine quadric      15.1.1 15.3 20.1.2
Affine space      2.1.1
Affine space, complex      2.8.7
Affine space, complexification of      7.6.2
Affine space, dimension of      2.1.8
Affine space, orientation of      2.7.2
Affine spaces, differential calculus in      2.7.7
Affine spaces, isomorphism between      2.2.6
Affine spaces, product of      2.2.2
Affine subspace      2.4.1 5.3
Affine subspaces, intersection of      2.4.2.4
Alexandroff      12.11.5.3
Alexandroff compactification      5.2.6 18.1.3.2 20.2.4
Algebra      0.2
Algebraic curves      16.4.9
Algebraic dual      0.2
Algebraic equations, solution by radicals      16.4.11.1
Algebraic geometry      4.0.5 4.2.6 12.7.5.1 17.1.6
Algebraic group      12.6.9
Algebraic hypersurface      14.1.4.2
Algebraic number field      13.1.4.5
Algebraic topology      4.0.5 4.3.7 4.3.9 12.7.5.3 II.86 18.8.7 19.1.3.3
Algebraic topology of orthogonal groups      8.10
Algebraic topology of projective spaces      4.3 4.8.2
Algebraic topology of the sphere      18.2.1
Algebraic varieties      14.1.6.2
Algebraically closed base field      6.4.2 6.5.1 6.7.2 6.7.4 13.4.3 13.5.3 14.1.5.3 14.1.6.2 16.2.10
Alhambra      1.7.1
Alternating bilinear form      2.7.2.1 14.8.12.2
Alternating group      0.2 1.8.4 6.3.2 12.5.5.6
Altitude of a spherical triangle      18.11.5
Altitude of a tetrahedron      10.6.6
Altitude of a triangle      9.4.1.3 10.1.4 10.13.1
Analysis      6.6 11.8.11.12 13.5.6 19.7.3
Analytic geometry      2.4.8 10.7.6 14.1.4 14.5.3 17.1.6
Analytic spheres      10.7.7 20.4.2
Angle between tangent vectors to a sphere      18.1.2.4
Angle of a rotation      1.7.5 9.3.4 9.3.5
Angle of an orientation-preserving similarity      9.6.3
Angle, dihedral      12.1.12
Angle, non-oriented      8.6
Angles and similarities      8.8.5
Angles in Artinian plane      13.8.5
Angles in Euclidean affine space      9.2.1
Angles in hyperbolic space      19.2.7
Angles of a spherical triangle      18.6.6
Angles of a triangle      10.1.2
Angles of a triangle, sum of      10.2.4
Angles of an elliptic triangle      19.1.8.1
Animals      12.5.5.7 11.86
Anisotropic      18.2.1 13.9.4
Antihomographies      18.10.2.4
Antir Euclidean      19.2.7
Appolonius      17.1.5 17.3
Appolonius’ formula.      9.7.6.1
Appolonius’ hyperbola      17.5.5.6
Appolonius’ problem      10.11.1
Appolonius’ Theorem      15.6.4
Approximation lemmas      12.9.2
Apulia, Italy      II.22
Arc cosine      8.3.11 9.9.7.1 18.6.6
Arc of circle      8.7.5.4
Archimedean field      8.5.2
Archimedes      15.7.6
Architecture      II.22 (see also “Shell architecture”)
Area      9.12.4.1 9.12.7
Area and Steiner symmetrization      12.10.10
Area of a compact convex set      12.10.2
Area of a triangle      9.7.3.8 9.12.4.4 10.1.5
Area of ellipse      17.7.5
Area of pedal triangles      10.4.5
Area of polytopes      12.8
Area of the sphere      12.10.4.1
Areas on the sphere      18.8.8.1
Areas, calculation of      9.12.6.3
Argument      8.7.9
Arithmetic      6.6 10.13.29 12.4.6 13.7.2 19.7.3
arrow      3.1.2
ART      I.ix 1.7.1
Artin      13.7.2
Artinian plane      13.1.4.4 13.8 19.2.5
Artinian space      18.1.4.4
Artinian space, quadrics in      14.4
Associativity of barycenters of punctual masses      3.4.8
Associativity of the base field      2.5.5 5.4.4
Asteroids      17.2.1.7
Astroid      9.14.34.8 17.7.4
Astronomy      II.146 18.6.1 18.6.11 18.6.13.8
Asymptote      15.5.11 17.8
Asymptotic cone      15.5.11
Atlas      4.2.1
automobile      18.6.11
Automorphic function      6.6.7
Axiomatic point of view      5.0.1
Axiomatization      2.6.7 2.5.5
Axiomatization of affine geometry      2.6.7
Axiomatization of Euclidean geometry      9.2.3
Axiomatization of projective geometry      4.5.12 4.6.7
Axis of a rotation      8.4.7.1 9.3.5
Axis of a screw motion      9.3.5
Axis of an ellipse      16.3.10.2
Axis of inertia      13.5.6
Bailing-out maxim      11.1.2.2
Balls, volume of      9.12.4.6
Barycenter      3.4.1 3.4.5 9.7.6 9.12.6.1 11.1.8.3
Barycenter coordinates      3.6.2 10.6.8 10.13.26
Barycenter subdivision      3.6.5 3.7.8
Barycenter, calculation of      3.4.6.6
Base field      see “Associativity” “Commutativity” etc.
Base of a pencil      14.2.7.3
Basel cathedral      9.6.9 9.14.32
Basis of a complexification      7.1.3
Beltrami      19.7.2
Bernoulli, Jakob      9.6.9
Bernoulli’s tomb      9.6.9 9.14.32
Betti numbers      4.3.9.4
Bezout’s Theorem      16.4
Bicircular quartics      9.6.8
Bieberbach’s isodiametric inequality      9.13.8
Bieberbach’s theorem      1.7.7.3
Bijections      0.2
Bilinear form      8.1.1 II.86
Billiards      9.4.1 9.14.9 17.9.2
Binet’s formula      17.2.1.7
Binomial coefficients      0.2
bisector      8.7.3.2 8.7.7.4 8.12.10 9.14.3 18.11.5 20.4.4 20.8.2
Bistochastic matrices      11.6.6.3 11.9.7
Bitangent conics      16.4.10.3
Blaschke Kugelungsatz      9.13.6 9.14.24
Blaschke rolling Theorems      12.12.14
Blaschke selection theorem      9.11.4
Blaschke — Lebesgue      12.10.5
Bolyai      19.7.2
Bonnesen’s theorem      12.11.9.4 12.12.15
Borsuk — Ulam, theorem of      18.2.7
Bound vector      2.1.3
box      9.12.4.2
Boy’s surface      4.3.9.1
Brahmagupta’s formula      10.13.7
Braid lemma      9.5.4.9
Brianchon’s theorem      16.2.13 19.3.5
British Museum      12.5.5.7
Bruhat — Tits lemma      9.8.6.5
Brunn — Minkowski theorem      11.8.8.1 12.11.3
Calculation in affine spaces      2.3.8 9.2.6
Calculation in projective spaces      4.2.1
Calculation of areas      9.12.6.3 12.10.11
Calculation of barycenters      3.4.6.6
Calculation of cross product      8.11.10
Calculation of cross-ratios      6.2
Calculation of duals      14.5.3
Calculation of projective morphisms      4.5.13
Calculation of quadrics      14.1.4
Calculation with affine polynomials      3.3.3
Calculation with vectors      3.1
Canonical density      8.11.8
Canonical measure of affine spaces      2.7.4.2
Canonical measure of elliptic spaces      19.1.1.7
Canonical measure of Euclidean affine spaces      9.12
Canonical measure of hyperbolic space      19.5.1
Canonical measure of spheres      12.3.2 18.3.7
Canonical norm      9.2.6.4
Canonical projection onto a projective space      4.1.1
Canonical topology of a projective space      4.8.1
Canonical topology of an affine space      2.7.1.1
Canonical volume      9.12
Canonical volume form      8.11.3 18.3.4
CAR      18.6.11
Caratheodory’s theorem      11.1.8.6 11.5.8 11.7.4.2
Cardboard polyhedra      12.1.3.2 12.8
Cardinality of a set      0.1
Cardioid      9.6.8 9.14.34.3 9.14.34.5
Caron, Joseph      I.xi
Cartan — Dieudonne Theorem      13.7.12
Carthage      12.11.8
Cartography      4.7.5 18.1 18.1.5.4
Cartography of France      18.1.8.5
Cartography of Switzerland      18.1.8.3
Cash prize      10.6
Castel del Monte, Italy      II.22
Castillon’s problem      10.11.4 16.3.10.3
Cauchy — Schwarz inequality      12.11.5.4
Cauchy’s formula      12.3.3 12.8.1 12.10.2 12.11.9.6
Cauchy’s Lemma      12.6.6.1 18.6.11 18.7.16
Cauchy’s Theorem      12.8.1
Caustic      9.14.34.3
Cayley      5.2.2 I.122 8.8.7.5 16.6.1 16.6.12.4
Cayley numbers      see “Octonions”
Cayley — Menger determinant      9.7.3.1 9.7.4 9.14.23
Cayley’s formulas      17.6.7
Celestial charts      18.1.8.6
Cell decompositions      4.3.9.4
Center of a compact set      2.1.5.5
Center of a group      1.6.7.2
Center of a quadric      15.5.3
Center of a regular polygon      12.4.3
Center of a regular polytope      12.5.2.1
Center of a rotation      1.7.5 9.8.4
Center of a similarity      9.5.2
Center of a sphere      10.7.1
Center of an isometry      9.3.3
Center of curvature      see “Curvature”
Center of mass      2.7.5.3 3.4.2 3.4.6.1 12.5.2.1
Center of the ortogonal group      8.2.16
Central field      8.1.2.2
Central quadric      15.5.3
Centrifugal "force"      17.5.5.5
Centroid      2.7.5.2 3.4.2 9.12.6 11.5.9.3 11.7.6
Ceva, theorem of      2.8.1 3.7.12 10.13.1.2
Chain of theorems      10.9.8 10.13.19
Change of variable theorem      0.6 2.7.4.2
Characteristic classes      14.3.7
Characteristic function      0.6
Chart      4.2.1 18.1.5.1 18.2.1 18.11.2
Chart, what you want in a      18.1.7
Charts in P(E)      4.5.13
Chasles circles      17.9.11
Chasles’s relation      2.1.5 8.7.2.4 10.9.7.2 16.6.1
Cheeger — Simons, conjecture by      18.3.8.6
Chinese lantern      9.12.7
chords      10.9.2.1
circle      8.3.3 8.12.4 9.4.4 10.7.1 11.6.1 18.1.8.1
Circle as a conic      17.4.2
Circle Limit      II.342
Circle, classical problems on      10.11
Circles in hyperbolic space      19.3.3.2 19.6.8.2
Circles in the plane      10.9
Circular group      20.6.1
Circular sections      15.7.14
Circumscribed      12.5.2.1
Class formula      1.6.6 1.8.3.1
Classical geometry      2.7 I.200
Classical groups      16.3.9
Classification      1.6.5
Classification of affine quadrics      15.3
Classification of crystallographic groups      1.9.9
Classification of Euclidean affine quadrics      15.6.1
Classification of quadratic forms      13.1.4.1 13.4
Classification of quadrics      14.1.5
Clifford algebra      8.9.13 8.10.3 13.6.8
Clifford parallelism      4.3.7 18.8.1.2 18.8.4 18.9.3 18.11.17 19.1.4
Clifford parallelism, generalizations of      18.9.4.4
Clifford parallelogram      18.8.4
Closed ball      0.3
Closed convex hull      11.2.3
Closed hyperplane      2.1.3.2
Closedness of stabilizers      9.8.3
Cobordism      4.0.5
Cocoon      11.3.6.0
Cocube      12.1.2.5 12.5.4.3
Cogwheel design      9.14.34.6
Cohomology rings      4.3.9.4
Combinations      1.5.2
comets      17.2.1.7
Common perpendicular      9.2.6.5
Commutative algebra      16.4.9
Commutativity of base field      2.3.3.9 2.5.5 4.5.6 4.9.8
Compact convex set      9.12.7 12.9
Compact manifolds      4.0.5
Compact subgroups of GA(X)      2.7.5
Compactness of orthogonal group      8.2.3.3
Compactness of projective spaces      4.3.3
Compactness of sphere      18.2.1
Compactness of stabilizers      9.8.6
compass      10.8.3 10.9 10.11.2
Complementary affine subspaces      2.4.9.4
Complete quadrilateral      3.7.18 6.4.4 17.9.19
Completely faithful      5.1.3
Completely singular      13.2.1
1 2 3 4 5 6
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