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Record Nr. |
UNINA9910139339203321 |
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Autore |
Bennett M. K (Mary Katherine), <1940-> |
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Titolo |
Affine and projective geometry / / M.K. Bennett |
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Pubbl/distr/stampa |
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New York, : Wiley & Sons, c1995 |
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ISBN |
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1-282-25339-5 |
9786613814043 |
1-118-03256-X |
1-118-03082-6 |
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Descrizione fisica |
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1 online resource (251 p.) |
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Disciplina |
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Soggetti |
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Geometry, Affine |
Geometry, Projective |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"A Wiley-Interscience publication." |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Affine and Projective Geometry; Contents; List of Examples; Special Symbols; Preface; 1. Introduction; 1.1. Methods of Proof; 1.2. Some Greek Geometers; 1.3. Cartesian Geometry; 1.4. Hilert's Axioms; 1.5. Finite Coordinate Planes; 1.6. The Theorems of Pappus and Desargues; Suggested Reading; 2. Affine Planes; 2.1. Definitions and Examples; 2.2. Some Combinatorial Results; 2.3. Finite Planes; 2.4. Orthogonal Latin Squares; 2.5. Affine Planes and Latin Squares; 2.6. Projective Planes; Suggested Reading; 3. Desarguesian Affine Planes; 3.1. The Fundamental Theorem; 3.2. Addition on Lines |
3.3. Desargues' Theorem3.4. Properties of Addition in Affine Planes; 3.5. The Converse of Desargues' Theorem; 3.6. Multiplication on Lines of an Affine Plane; 3.7. Pappus' Theorem and Further Properties; Suggested Reading; 4. Introducing Coordinates; 4.1. Division Rings; 4.2. Isomorphism; 4.3. Coordinate Affine Planes; 4.4. Coordinatizing Points; 4.5. Linear Equations; 4.6 The Theorem of Pappus; Suggested Reading; 5. Coordinate Projective Planes; 5.1. Projective Points and Homogeneous Equations in D3; 5.2. Coordinate Projective Planes; 5.3. Coordinatization of Desarguesian Projective Planes |
5.4. Projective Conies5.5. Pascal's Theorem; 5.6. Non-Desarguesian |
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Coordinate Planes; 5.7. Some Examples of Veblen-Wedderburn Systems; 5.8. A Projective Plane of Order; Suggested Reading; 6. Affine Space; 6.1. Synthetic Affine Space; 6.2. Flats in Affine Space; 6.3. Desargues' Theorem; 6.4. Coordinatization of Affine Space; Suggested Reading; 7. Projective Space; 7.1 Synthetic Projective Space; 7.2. Planes in Projective Space; 7.3. Dimension; 7.4. Consequences of Desargues' Theorem; 7.5. Coordinates in Projective Space; Suggested Reading; 8. Lattices of Flats; 8.1. Closure Spaces |
8.2. Some Properties of Closure Spaces8.3. Projective Closure Spaces; 8.4. Introduction to Lattices; 8.5. Bounded Lattices: Duality; 8.6. Distributive, Modular, and Atomic Lattices; 8.7. Complete Lattices and Closure Spaces, Suggested Reading; Suggested Reading; 9. CoIIineations; 9.1. General CoIIineations; 9.2. Automorphisms of Planes; 9.3. Perspectivities of Projective Spaces; 9.4. The Fundamental Theorem of Projective Geometry; 9.5. Projectivities and Linear Transformations; 9.6. CoIIineations and Commutativity; Suggested Reading; Appendix A. Algebraic Background; A.l. Fields |
A.2. The Integers Mod nA.3. Finite Fields; Suggested Reading; Appendix B. Hilbert's Example of a Noncommutative Division Ring; Suggested Reading; Index |
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Sommario/riassunto |
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An important new perspective on AFFINE AND PROJECTIVE GEOMETRYThis innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view.Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce l |
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