Geometry ISpringer Science & Business Media, 2009 M01 21 - 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. |
Common terms and phrases
affine frame affine geometry affine plane affine space algebraic apply arbitrary barycenter basis bijection bisectors called chapter circle collinear points compact set complex complexification consider construction containing convex function convex set coordinates COROLLARY cross-ratio curve defined definition denoted dimension elements equivalent Euclidean affine space Euclidean plane Euclidean space Euclidean structure Euclidean vector space example exists a unique Figure finite finite-dimensional fixed point formula function GA(X geometry GL(E homeomorphic homography homothety Idɛ intersection invariant inverse Is(X isometry isomorphism Lebesgue measure lemma linear map f map ƒ metric space morphism n-dimensional non-empty notation orbit oriented angles orthogonal orthonormal path-connected projective line projective space Proof PROPOSITION real number resp result rotation satisfying scalar Show sphere subgroup supporting hyperplane tangent theorem tilings triangle vector subspace