Geometry IISpringer Science & Business Media, 2009年1月21日 - 406 頁 This is the second of a two-volume textbook that provides a very readable and lively presentation of large parts of geometry in the classical sense. For each topic the author presents a theorem that is esthetically pleasing and easily stated, although the proof may be quite hard and concealed. 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. |
內容
Volume | 1 |
Barycenters the universal space | 3 |
Euclidean vector spaces | 8 |
Polytopes compact convex sets | 12 |
Projective quadrics | 13 |
The sphere for its own sake | 18 |
Quadratic forms | 86 |
Index | 106 |
applications | 111 |
Projective lines crossratios homographies | 174 |
Triangles spheres and circles | 256 |
| 375 | |
| 376 | |
| 381 | |
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常見字詞
acts transitively affine quadrics affine space angles arbitrary Art2 basis bijection chapter circle circumscribed Clifford parallels compact completely singular cone conjugate containing convex set coordinates COROLLARY cross-ratio curve deduce defined definition degenerate conics denoted dimension edges ellipse equation equivalent Euclidean space example exists faces Figure fixed follows form q formula geometry given homeomorphic homography hyperbola hyperbolic geometry hyperplane im(a inscribed intersection invariant involution isometry isomorphic isotropic isotropic lines lemma lines matrix metric non-degenerate non-empty image orbits orthogonal pairs parabola particular pencil of conics plane polar polygons polyhedra polyhedron PQ(E Proof proper conic proper quadric PROPOSITION quadratic form quadric regular polytope resp respect satisfying Show sphere spherical triangle subset subspace tangent tangential pencil theorem unique vector space vertex vertices volume