Projective Geometry and Projective Metrics
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.
Topics include the projective plane, polarities and conic sections, affine geometry, projective metrics, and non-Euclidean and spatial geometry. Numerous figures appear throughout the text, which concludes with a bibliography and index.
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affine geometry affine plane angle arbitrary asymptotes axes axis called carries circle Clifford parallels collinear collineation congruent conic contains convex curve convex set coordinate system cosh cross ratio deﬁned deﬁnition denote determined distance distinct points ellipsoid elliptic elliptic geometry equation Euclidean geometry exists expressed fact Figure ﬁnd ﬁrst ﬁxed points follows given harmonic homology hence Hilbert geometry hyperbolic geometry hyperparallels identity implies induced inﬁnity interior point intersection point invariant involution isometric mapping metric space Minkowski Minkowski metric Minkowskian motion no-tangent points non-collinear non-degenerate numbers obtained one-to-one parabola parallel pencil perpendicular perspectivity polar pole projective coordinates projective geometry projective metric projective plane projective-metric proof quadric radius reﬂection regulus representation respectively rotation satisﬁes Section segment self-polar shows sides sinh sphere straight line strictly convex supporting lines tangent tanh theorem transformation translation triangle triangle inequality triple unique yields zero