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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
Polyhedra, cardboard      12.1.3.2 12.8
Polyhedra, convention about      12.1.6
Polyhedra, pictorial representation of      12.1.3.3
Polyhedra, regular      1.8 12.5
Polyhedra, structure of      12.1.5
Polyhedron      12.1.8.1
Polynomial      3.3.1 3.3.5
Polynomial map      3.3.1 3.3.5
Polyspheric coordinates      20.7
Polytope      12 12.1.1
Polytope, area of      12.2
Polytope, volume of      12.3
Poncelet continuity principle      7.0.3
Poncelet theorem, great      10.10.4 10.13.3 16.5.5.3 16.6 17.6.5
Poncelet theorem, little      17.2.1.6 17.6.3.6
Positive alternating form      2.7.2.2
Positive definite quadratic form      8.1.1 11.1.2.8 11.8.11.2
Positively oriented basis      2.7.2.2
Positively oriented frame      2.7.2.10
Power of a point with respect to a sphere      10.7.10
Prestressed concrete      II.131
Principal circle      17.2.2.6
Principal hyperbolic arc-cosine      0.5
Principle of similar figures      9.6.7
Privileged unit of length      8.8.1
Problems of minimum      10.4
Product of affine spaces      2.2.2
Product, semidirect      2.3.3.7
Proficiency of students      10.6
Projection      2.4.9.6
Projective base      4.4.1
Projective completion      5.0.1 5.1.3 7.0.2 17.4.1
Projective coordinates      6.5.10
Projective group      4.5.9 4.9.5
Projective isomorphism      4.5.2
Projective line      4.6.2 6.6 6.8.15
Projective model      19.2.5
Projective morphism      4.5.2 4.5.13
Projective orthogonal group      8.7.7.1
Projective plane      4.6.2
Projective point      4.6.2
Projective quadric      14.1.1 14 18.10.1
Projective space      4.1.1 7.0.1 7.5.1 8.9.3 9.1.7
Projective subspace      4.6.1 4.6.15 5.3
Proper motion      9.1.4
Proper quadric      14.1.1 15.1.3.2
Ptolemaic dynasty      12.5.5.7
Ptolemy’s theorem      9.7.3.8 10.9.2
Pullback of a quadratic form      18.1.8.9
Punctual mass      8.4.5
Punctured plane      9.9.4.3
Pure quaternion      8.9.1 8.11.18
Purism      4.1.2
Pyramid      12.2.1
Pythagorean Theorem      9.2.3 10.2.3
Quadratic extensions      7.0.6
Quadratic fields      12.6.8
Quadratic form      8.8.2 4.0.5 8.8.6 9.5.5 11.8.11.2 13 18.1.1
Quadratic transformation      16.5.8.2 16.8.24
Quadric      10.7.4 4.0.5 4.1.3.6 “Projective”)
Quadric at infinity      15.1.8.2
Quadric of revolution      17.9.19
Quadric, group of a      14.7
Quadrics in $Art_{4}$      14.4
quantum mechanics      4.0.6
Quantum quartic      9.6.8
Quasi-spherical set      11.7.5
Quasi-symmetric set      11.7.5
Quaternionic projective spaces      9.1.7
Quaternions      0.2 2.6.4 4.8.2 4.9.7 8.9 8.9.1 8.11.13 8.12.11 12.6.10.2 18.8.8
Quetelet      17.3
Quintic equation      12.6.10.3
Radical      13.9.1 14.1.7 18.2.1
Radical axis      10.7.10.1 10.10.1
Radical center      10.7.10.2 10.11.1
Radical hyperplane      10.7.10.1
Radius of a sphere      10.7.1
Radius of curvature      see “Curvature”
Radius zero      20.1.8
Radon      11.7.4.1
Rank of a quadratic form      18.2.1
Rank of a quadric      14.1.1 15.1.8.2
ratio      2.8.8.9 8.8.2 9.5.1
Rational function      4.2.6
Rational numbers      0.2 13.1.4.5
Real affine spaces      2.7
Real numbers      0.2
Real projective spaces      9.1.7
Real proper quadrics      14.3.2
Real vector spaces      7.0.1
Rectillable curve      9.9.1 12.11.6.1
Reduced quadric      15.6.1
Reeb foliation      18.8.7
Reflection      2.4.9.6 6.4.6 8.2.9 9.2.4 13.6.6.1 19.1.2.4
Reflection axis      9.8.4
Regular octagon      II.22
Regular pentagon      12.5.5.2 12.12.4
Regular poly tope      12.5 12.5.1 12.6 12.12.7
Regular polygon      12.4 12.4.1
Regular polyhedron      1.8 12.5 12.12.10
Regular polyhedron, hyperbolic      19.8.26
Regular simplex      12.5.4.1 11.5.8 12.1.2.5
Relative interior of a convex set      11.2.8
Relativity      19.7.3 13.1.3.2
Representation      8.12.13
Restriction of a map      0.1
Restriction of a quadratic form      13.1.3.5
Reuleaux triangle      11.5.9.2
reversing      9.5.4.2
Reversing similarities      9.5.1
Ricatti equation      6.8.12
Riemann sphere      6.8.8 18.1.3.2 4.2.5
Riemannian geometry      9.10.7 18.6.11
Riemannian manifold      9.9.6 9.10.7 18.3.8.6 18.10.9 11.3.9
Riemannian manifolds      12.7.5.2
Riemannian metric      19.7.2
Riemannian metrics      13
Right      10.1.3
Right angle      8.7.3.5 8.7.7.4
Right translation      1.2.6
right triangles      9.6.8.2
Rigid motions      9.1
Roger Penrose      1.9.16
Rolling theorems      12.12.14
Roof      10.6.8.1
Roofs      10.6.8
Root      16.4.1
Rotation      13.6.3 8.2.1
Rotation in three dimensions      9.3.5
Rotation of a Euclidean plane      1.7.5
Rotation of finite order      1.8.1
Rotation, plane      9.3.4
Rotation, three-dimensional      8.4.7.1 8.9.5
Ruled surface      6.8.20
Ruler      10.8.3 10.9 10.11.2 12.4.6
Salmon’s principle      10.13.14
Scalar product      8.1.1
Schlaefli      12.6
Schlaefli’s theorem      12.6.7
Schmidt, E.      12.11.5.3
Schwarz inequality      8.11.7
Screw motion      9.3.5 9.14.7
Search for maxima      11.8.10.10
Secant      10.7.5
Secant spheres      20.4.2
Second barycentric subdivision      3.6.5
Second fundamental theorem of projective geometry      5.4.8
Second variation formula      9.10.7
Second-order formulas      18.6.13.8
Section of a group action      1.6.6
Sector      8.7.5.4
Segment      6.8.14 9.9.4.1 3.4.3
Segments of conics      19.8.11
Self-devouring reptile      3.1.9
Self-polar      14.5.4.1 16.4.10.1
Self-polar simplex      13.5.4.2 14.5.4
Self-polar triangle      14.8.11 10.13.24
Semiaffine map      2.6.2
Semidefinite quadratic form      11.8.11.2
Semidirect product      2.3.3.7
Semilinear map      6.4.10 7.1.2.1 7.7.2 2.6.2
Semimorphism      6.4.9 7.5.2
Semisimple Lie group      8.12.13
Semisimple Lie groups      1.8.7.3
Sending objects to infinity      5.4
Separates      11.4.3
Separation theorems      11.4
Sesquilinear      14.8.12.2
Set, cardinality of a      0.1
Sets, difference of      0.1
Seven circle theorem      10.11.7
Shaddock      12.7.5.1
Shell architecture      14.4.6 15.3.3.3 15.3.3.3
Shepherd principle      1.5.8
Shortest path      6.8.14 9.9.5
Shortest paths in elliptic spaces      19.1.2.1
Shortest paths on the sphere      18.4.2
Side of a polyhedron      12.1.5 12.1.8
Side of a triangle      10.1.2
Sides of a spherical polygon      18.7.3
Sides of a spherical triangle      18.6.6
sides of a triangle      2.4.7
Sides of elliptic triangle      19.1.3.1
Sign flips      18.7.15
Signature      13.4.7
Signed area      10.4.5.1
Similarities      8.8 9.5.1 9.14.12
Similarities and angles      8.8.5
Similarities and complexifications      8.8.6
Similarities, characterization of      9.5.3
Similarity      8.8.2
Similarity of triangles      10.2.7
Simple closed curve      12.11.6.1
Simple field      8.5
Simple Lie groups      12.6.8
simplex      14.5.4.1 11.6.1 2.4.7 3.7.8
Simplex, solid      12.1.2.2
Simplicity of O(E)      8.5
Simplicity of orthogonal groups      13.6.8
Simply connected      12.7.5.3
Simply transitive abelian group      8.7.2.5
Simply transitive action      1.4.3
Simson line      17.4.3.5 17.8.3.2 10.4.5.4 10.9.7 10.11.3 10.13.27
Simultaneous orthogonalization      13.5
Sine      8.3.6
singular      14.1.7 13.2.1
Singularities of diflerentiable maps      12.6.8
Sink      18.10.2.3
Six-pointed shaddock      12.7.5.1
Sixth circle, theorem of      10.7.10.3
Skew base field      6.3.3
Skew field      4.8.1 6.1.7 6.8.13 6.8.15 6.8.18
Skew field, finite      1.6.7.3
Skew fields      2
slope      16.7.1.1
Smooth point      11.6.1
Snake that bites its tail      3.1.9
Sobolev spaces      11.86
soccer balls      12.4.6
Solid ellipsoid      11.8.9.1
Solid simplex      9.12.4.2 12.1.2.2
Soup bowl      8.10.3
Source      18.10.2.3
South pole      18.1.2.3
Space of generalized spheres      20.1.5
Spain      1.7.1 14.4.6
span      4.6.5 2.4.2.5
Special affine group      2.7.6
Spencer — Glaezer joint      18.11.16
Sphere      9.5.3.1 9.7.4 9.9.4.3 10.7 10.7.1
Sphere $S^{4}$      4.9.7
Sphere $S^{8}$      4.8.3
Sphere as a projective quadric      18.10.1
Sphere as affine quadric      20.1.2
Sphere circumscribed around the regular simplex      11.5.9.1
Sphere of radius zero      20.1.8
Sphere, area of the      12.10.4.1
Sphere, canonical measure on      12.3.2
Spheres      9.1.7 18 1.6.4
Spheres of non-zero imaginary radius      20.1.8
Spheres, group structure on      8.9.1
Spheric mirror      9.14.34.3
Spherical conic      18.11.15
Spherical digon      18.3.8.2
Spherical geometry      1.8.6
Spherical harmonics      12.11.9.4
Spherical helices      9.14.34.3
Spherical helix      18.3.3
Spherical quadrilaterals      18.11.12
Spherical triangle      12.5.5.2 18.6.2 19.8.25
Spherical triangles      18.6
Spherical trigonometry      12.5.5.2 18.4.4.1 18.6.1
Spherical zone      12.12.20.2
Spherometer      18.1.1 18.11.1
Spinor      8.10.3
SPLINE      15
Stabilizer      9.8.1 1.5 1.5.1
Stabilizer of a regular polygon      12.4.3
Stabilizer of a tile      1.7.5.1
Standard cocube      12.1.2.5
Standard cube      12.1.2.5
Standard n-dimensional Euclidean affine space      9.1.2
Standard projective space      4.1.8.1
Standard simplex      12.1.11.1
Standard solid simplex      12.1.2.5
Standard tile      1.7.2
Star polytopes      12.6.10.5
Star regular polytopes      12.12.8
Star-shaped      11.1.2.4 11.3.6 11.7.6 11.9.6 11.9.20
Starting point      9.9.1
Steiner symmetrization      9.13 9.18.1 11.1.4 12.10.10 12.11.2 12.12.1
Steiner — Minkowski      12.11.3
Steiner — Minkowski formula      12.3.5 12.10.6
Steiner — Minkowski theorem      12.10.6
Steiner’s alternative      10.10.3
Stereocomparator      4.7.5
Stereographic projection      4.3.8 8.7.6 11.3.6.5 18.1.4.1 18.1.8.6 18.9.1 18.10.2 18.10.3.2 18.11.3 19.6.11
Stewart relation      9.14.35
Stokes’ Theorem      12.11.4
Straightedge      see “Ruler”
Strasbourg      10.12.1
Strict triangle inequality      see “Triangle inequality”
Strictly convex function      11.8.5
Strictly convex set      11.6.4
Strictly separated      11.4.8
String construction      15.7.16 17.2.2.5
String toy      17.6.4
Strip of paper      17.7.1
Strongly ergodic      9.4.4
Submanifold      14.3.8 15.4.5
Subnormal to a parabola      17.9.18.1
Subsphere      18.1.2.1
Successive differences      12.10.6
Sum of angles of a polygon      10.5.2
Sum of angles of a triangle      1.8.6 10.2.4
Sum of squares      11.87
Sum, direct      0.2
Sun      17.2.1.7
Superosculating conics      16.4.5 16.4.10.5 19.6.8.3
Supporting function      11.8.12.8 11.9.14
1 2 3 4 5 6
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