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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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Least-perimeter triangle      10.4.4
Lebesgue measure      0.6 2.7.4.3 8.2.5.2 9.12.1 11.8.8.1 12.2.5
Lebesgue, Henri      I.xi
Lefschetz fixed point theorem      18.2.5.7
Left translation      1.2.6 1.4.4.2
Length of a compact convex set      12.10.2
Length of a curve      9.9.1 9.12.4.1 12.11.6.1 19.8.18
Length of ellipse      17.7.5
Length of hypo- or epicycloid      9.14.34.4
Lens      6.8.4 18.1.1
Lever      18.11.1
Lexell’s theorem      18.11.10
Lhuillier, Simon      18.6.13.8
Lhuillier’s inequality      12.12.16
Lie algebra      8.12.9
Lie group      1.8.7.3 2.7.5.12 8.10.1 12.6.8
Light cone      13.2.1
Light polygon      9.4.1 9.4.2
Limit points of a pencil of circles      10.10.1
Lindeloef      12.11.9.2
Line in elliptic space      19.1.1.5
Line in hyperbolic space      19.2.10
Line of position      18.6.11
Line of the images      17.6.2.2 10.13.16
Line, affine      2.1.8 2.4.2.1
Linear algebra      4.6.8 11.7.4.1 2.4.8 4.0.5
Linear equations, system of      2.2.3
Linear group      0.2 1.2.4
Linear maps      0.2
Linear programming      11.8.10.10
Link of a regular polytope      12.5.3.2
Linkedness      14.3.4 10.12.2 20.5.5
Liouviile      9.5.4.21
Liouviile form      11.87
Liouviile’s theorem      9.5.4 10.8.5.4
Lipschitz map      9.11.5 9.11.6
Little circle      18.1.2.2
Little sphere      18.1.2.2
Live edges      12.8.6.4
Live face      12.8.6.4
Live vertices      12.8.6.4
Living creature      12.5.5.7
Lobatchevsky      19.7.2
Local convexity      11.1.7.4
Locally compact field      4.3.5
Loewner — Behrend function      11.8.9
Loewner — Behrend theorem      11.8.10.7
Logarithmic spiral      9.6.9.1 9.14.21 9.14.32 17.9.16 18.11.3
Lohr, Germany      14.4.6 15.3.3.3
longitude      18.1.6.1
Lorentz group      13.6.1 19.7.3
Lorentz metrics      13
Lower Minkowski area      12.10.9.3
Loxodrome      18.1.8.2 18.3.3 18.11.3
Loxodromes      18.3.3
Lucas theorem      11.9.21
Lueroth      16.2.10
l’Oeuvre Notre-Dame museum (Strasbourg)      10.12.1
Major axis      17.2.1.4
Malfatti’s problem      10.11.5
Manifold      see “Differentiable”
Map, identity      0.1
Map, restriction of a      0.1
Marchaud      15.4.8
Mathematical zoo      11.86
Matrix associated to a quadratic form      13.1.3.6
Matrix, identity      0.2
Matrix, transpose of a      0.2
Maximal width      11.9.12
Maximum perimeter polygons      17.6.5 17.9.7
Measure of an angle      18.8.5 8.3.9 8.4.3 8.7.7.6
Measure of an oriented angle      8.7.4.1
Measure theory      11.6.6.2
Measure zero      12.3.3.1 9.4.4 11.3.2
Measuring angles, difficulty in      8.3.13
Mechanical devices      12.10.5
Mechanical generation for ellipses      17.7.1
Mechanical linkage      4.9.12 10.8.3
Mechanics      2.7.5.3 3.4.2 3.4.6.1 8.9.5 9.14.34.6 II.87 17.5.5.5 II.255 18.6.1
Median      3.4.10 10.1.4
Median of a spherical triangles      18.11.5
Median of a tetrahedron      10.6.3
Menelaus, theorem of      2.8.2 3.7.17
Menger      9.7.4
Menger curvature      9.14.31
Mercator projection      18.1.8.2 18.10.3.2
Meridian      10.12.1 18.1.6.2
Meridian of a torus      18.8.6 18.9.3
Meromorphic functions      9.5.4.8 18.1.3.2
Metric spaces      0.3
Metrical properties of conics      17.2 17.3 17.4
Metrical properties of elliptic space      19.1.2
Mexico      15.3.3.3
midpoint      3.4.2 3.4.10 6.4.2 19.4.3
Miguel’s six circle theorem.      10.9.7.2
Minimal width      11.5.9.5 11.9.12
Minimum, problems of      10.4
Minkowski      12.3.4 11.9.16
Minkowski area      12.10.9.3
Minkowski geometry      15.5.10
Minkowski inequality      11.8.11.10
Minkowski sum      12.1.17 11.1.3 11.9.1 11.9.14
Mirror      6.8.4
Mixed product      8.11.8
Moebius group      18.10.1.4 18.10.2 18.11.21 19.2.2 19.4.6.4
Moebius invariant      18.10.8
Moebius tetrahedra      4.9.12 5.5.3 14.5.5 10.6.7
Mohr — Mascheroni, Theorem of      10.11.2
moment      14.8.12.5
Moment of inertia      9.12.6.3
Moral of the story      6.2.6
Morley      9.14.38
Morley’s theorem      9.14.34.5 10.3.10 10.13.4
Morphism, affine      2.3
Mostow’s rigidity theorem      18.10.9
Motions      9.1.4
Motzkin theorem      11.1.7.2
Movie projectors      12.10.5
MTU      18.1.5.3
Multilinear map      7.3.1
Multiplicity of an intersection      16.4.9
Multivalued algebraic correspondence      16.6.1
Museum      I.ix 11.7.6
Mystic hexagon      16.2.12
Nagel’s point      10.13.30
Napier’s analogies      18.6.13.8
Napoleon — Mascheroni, problem of      10.11.2
Napoleon’s theorem      9.14.44
Naturality      7.0.3
Navigation      18.6.1 18.6.11
Nephroid      9.14.34.3
Neutral quadratic form      18.1.4.8
Nevanlinna      9.5.4.7
New Zealand      18.1.8.6
Newton’s laws      17.2.1.7
Nine-point circle      17.5.4 10.11.3
Nine-point conic      16.7.5
Non-associativity of barycenters      3.4.9
Non-degenerate form      18.2.1
Non-degenerate quadric      10.7.11
Non-Euclidean geometry      1.8.6
Non-negative integers      0.2
Non-negative reals      0.2
Non-oriented angles      8.6.3 13.8.7
Non-periodic hyperbolic tilings      19.6.12
Non-periodic tiling      1.7.2 1.9.16
Non-rectifiable curve      9.9.3.3 12.12.9
Non-regular tiling      1.7.2
Non-singular      18.2.1
Non-singular completion      18.8.4.1
Norm      8.1.1 11.8.12.1
Norm of a quaternion      8.9.1
Norm, canonical      9.2.6.4
normal      17.1.4
Normal cone      11.6.2
Normal endomorphism      8.12.5
Normal to a conic      17.5.5.6
Normal to a parabola      17.9.18.2
Normal to a quadric      15.7.15
Normalization      8.1.4
North pole      18.1.2.8
Notion of a geometry      1.4
Nullstellensatz      14.1.6 15.7.1
Number of holes      12.7.5.4
O(E), center of      8.2.16
O(E), compactness of      8.2.3.3
O(E), simplicity of      8.5
O(q), involutions of      13.6.6
Object focal point      6.6.4
Oblique Mercator projection      18.1.8.8
Obtuse      10.1.8
octahedron      1.8.4 12.5
Octonionic projective plane      9.1.7
Octonions      2.6.7 4.8.3 8.9.1 18.1.3.5
One-dimensional diiferentiable manifolds      11.3.10.1
One-sheet hyperboloid      15.8.8.8 11.132
One-sphere      4.3.6
Open ball      0.3
Open hyperplane      2.7.3.2
Opposite half-line      8.6.1
Optics      6.6.5 9.14.34.6
Orbit      1.6.1
Order of a point      11.6.1
Order of a root      16.4.2
Orientation-preserving map      2.7.2.5 9.5.1 9.5.4.2 8.8.2
Orientation-reversing      see “Orientation-preserving”
Oriented angle      8.7.2.3 8.7.7.2 9.2.1
Oriented sphere      20.6.4
Oriented triangle      10.4.5.1
Origin as a distinguished point      2.2.3
Ort honormal      8.1.1 9.1.1
orthocenter      10.2.5
Orthochronous rotation      13.8.3
Orthogonal affine subspaces      2.4.8.1
Orthogonal direct sum      8.1.8.4
Orthogonal group      8.2.1 12.6.8 13.6.1
Orthogonal groups, algebraic topology of      8.10
Orthogonal groups, simplicity of      13.6.8
Orthogonal projection      9.2.4 9.12.4.9
Orthogonal projective group      14.7.2
Orthogonal reflection      8.2.9
Orthogonal spheres      10.7.7
Orthogonal subspaces      9.2 13.3.1
Orthogonality      9.2.1
Orthogonality in Euclidean spaces      8.1.1
Orthogonalization      13.4
Orthogonalization, simultaneous      13.5
Orthonormalization      8.1.4
Orthoptic circle      16.2.7.1 17.4.2.3 17.6.1 17.9.5
Orthoptic sphere      15.7.13
Osculating circle      10.8.5.5 17.5.5.4
Osculating conics      16.4.5 16.4.10.4 16.4.13
Osculating curves      16.4.12
Outer automorphism      8.10.2
Outside      18.2.6.2
Overcrowding      19.8.21
p-group      1.6.7 1.6.7.1
p-transitive action      1.4.5
Pacioli, Fra Luca      I.26 II.3
painting      12.3.8 9.12.7
Paper band      8.10.3
Pappus’s theorem      2.5.3 2.8.9 5.4.1 5.4.2 16.2.12 16.8.19
parabola      1.4.2 9.6.7.2 10.13.18 15.3.3.2 15.7.6 17.5.5.5 17.9.18
Parabola tangent to four lines      16.7.4
Parabolas and the Simson line      17.4.3.5
Paraboloid      15.3.3.3 15.5.3
Parallel affine subspaces      2.4.9.1
Parallelepipeds      9.7.3.1 12.1.2.1
Parallelism      4.6.13 5.3
Parallelogram rule      8.7.2.5 2.5.2 2.6.6.4
Parallels of latitude      10.12.1 18.1.6.2
Parallels on the torus      18.9.3
Paratactic annulus      10.12.3
Parataxy      10.12 18.9
Pascal limagon      9.6.5 9.14.17 9.14.22
Pascal line      16.8.3
Pascal, Blaise      9.6.8
Pascal’s theorem      16.2.11 16.8.4 16.8.5 2.8.2
Path      9.9.1
Path-connectedness of circle      8.12.4
Path-connectedness of projective spaces      4.3.3
Path-connectedness of sphere      18.2.1
Path-connectedness of U      8.3.8
Peano curve      18.2.4.1
Pedal curve      9.6.8 17.2.2.6
Pedal triangle      10.4.5
Pencil of circles      10.10 10.10.1
Pencil of conics      6.7.4 16.5 16.8.15 17.5.1
Pencil of hyperplanes      6.5.1
Pencil of lines      6.5.1
Pencil of planes      6.5.1
Pencil of quadrics      14.2.6
Pencil of spheres      20.5
Pendulum      17.5.5.5
Pentaspheric coordinates      20.7.1
Perimeter      9.4.1 9.4.2 12.3.1
Permutation      1.5.2 1.6.4
Permutation group      0.2
Permutation matrices      11.6.6.3 11.9.7
Perpendicular bisector      9.7.5.1 18.11.5
Perpetual motion      1.7.4
Perspective      4.7 4.7.3
petersen      9.14.38
Physical universe      8.8.1 8.11.7 I.200 12.10.11.2
Physics      8.9.5 II.146
Pitch      9.3.7
Pivot      10.13.18
Plane curves      8.2.14 12.11.9.4
Plane diopter      6.8.4
Plane isometries      9.3.4
Plane lattices      9.14.29
Plane projective      4.1.3.3
Plane similarities and complex numbers      8.8.4 9.6
Plane, affine      2.1.8 2.4.2.1
Planet      17.2.1.7
Plate, homogeneous      2.7.5.3 3.4.2
Plato      12.5.5.7
Pluecker’s theorem      16.5.6.3
Poincare      19.7.1
Poincare metric      19.6.10
Poincare model      19.6
Point at infinity      4.0.2 5.2.3 5.3 10.7.11 15.1.3.2 20.1.8
Point, affine      2.1.8 2.4.2.1
Point, projective      4.1.3.3
polar      6.5.7 14.5.1 13.3.2
Polar body      11.1.5.1 12.1.2.6 12.12.2
Polar cone      18.11.15
Polar form      8.7.9 3.3.2 13.1.1 13.9.8
Polar hyperplane      14.5.1 15.5.1
Polar line      see “Polar”
Polar of a point with respect to two lines      6.5.7
Polar quadric      14.6.4
Polar regions      18.1.8.6
Polar triangle      18.6.12.1 19.8.3
Polarity      10.7.11 14.5
Polarity with respect to a quadric      15.5.1
Pole      14.5.1 18.1.2.3
Polygon      2.8.13 10.5 12.1.1 18.7.1
Polygonal billiards      9.4
Polyhedra      12
1 2 3 4 5 6
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