Geometry I

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Springer Science & Business Media, Jan 21, 2009 - Mathematics - 432 pages

Volume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern literature, providing a unified reference to geometry in the full breadth of its subfields and ramifications.

 

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Contents

examples and applications
4
Affine spaces
32
Barycenters the universal space
67
Projective spaces
85
applications
111
Projective quadrics
116
Projective lines crossratios homographies
122
Complexifications
142
Euclidean conies
218
The sphere for its own sake
255
Triangles spheres and circles
279
Elliptic and hyperbolic geometry
318
Convex sets
331
The space of spheres
349
Bibliography
363
Index of notations
379

Affine quadrics
146
Euclidean vector spaces
151
Projective conics
170
Euclidean affine spaces
200

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