Introduction to Projective GeometryCourier Corporation, 12.09.2011 - 576 Seiten This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals. |
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Häufige Begriffe und Wortgruppen
A₁ affine transformation angle arbitrary line arbitrary point asserted Axiom axis B₁ base points C₁ coefficients collinear points collineation of type complete four-point concurrent concurrent lines Corollary corresponding points cosh cross ratio d₁ d₂ defined Definition Desargues determined diagonal points elements elliptic geometry euclidean geometry euclidean plane Exercise F₁ fixed points following theorem gauge points given harmonic conjugate harmonic tetrad Hence homogeneous coordinates hyperbolic hyperbolic geometry ideal line intersection involution involutory hexad k₁ l₁ l₂ Lemma line-conic linear locus M₁ M₂ matrix metric gauge conic multiplication nonsingular conic nonsingular point-conic P₁ P₂ pairs of corresponding parameters parametrized in terms Pascal's theorem pencil plane perspective polar projective geometry projective plane Proof Let properties real points satisfy self-corresponding Show sinh T₁ tangent theorem of Pappus transformation V₁ vanishing line vector vertices x₁ XTAX Y₁ zero