LEADER 04732nam 2200613Ia 450 001 9910139339203321 005 20170810194816.0 010 $a1-282-25339-5 010 $a9786613814043 010 $a1-118-03256-X 010 $a1-118-03082-6 035 $a(CKB)2560000000060928 035 $a(EBL)661621 035 $a(OCoLC)705538687 035 $a(SSID)ssj0000482599 035 $a(PQKBManifestationID)11308146 035 $a(PQKBTitleCode)TC0000482599 035 $a(PQKBWorkID)10526495 035 $a(PQKB)10215821 035 $a(MiAaPQ)EBC661621 035 $a(PPN)250260166 035 $a(EXLCZ)992560000000060928 100 $a19941117d1995 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAffine and projective geometry$b[electronic resource] /$fM.K. Bennett 210 $aNew York $cWiley & Sons$dc1995 215 $a1 online resource (251 p.) 300 $a"A Wiley-Interscience publication." 311 $a0-471-11315-8 320 $aIncludes bibliographical references and index. 327 $aAffine 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 327 $a3.3. 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 327 $a5.4. Projective Conies5.5. Pascal's Theorem; 5.6. Non-Desarguesian 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 327 $a8.2. 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 327 $aA.2. The Integers Mod nA.3. Finite Fields; Suggested Reading; Appendix B. Hilbert's Example of a Noncommutative Division Ring; Suggested Reading; Index 330 $aAn 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 606 $aGeometry, Affine 606 $aGeometry, Projective 615 0$aGeometry, Affine. 615 0$aGeometry, Projective. 676 $a516.4 676 $a516/.4 700 $aBennett$b M. K$g(Mary Katherine),$f1940-$0521914 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139339203321 996 $aAffine and projective geometry$9835332 997 $aUNINA