Projective Geometry and Algebraic Structures
- 1st Edition - January 1, 1972
- Imprint: Academic Press
- Author: R. J. Mihalek
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 3 5 5 - 9
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 5 2 0 - 9
Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers.… Read more
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Request a sales quoteProjective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.
PrefaceAcknowledgmentsChapter 1 Introduction 1.1 Euclidean Planes 1.2 Incidence Bases 1.3 Set TheoryChapter 2 Affine Planes 2.1 Axioms for an Affine Plane 2.2 ExamplesChapter 3 Projective Planes 3.1 Axioms for a Projective Plane 3.2 Examples 3.3 Algebraic Incidence Bases 3.4 Self-Dual AxiomsChapter 4 Affine And Projective Planes 4.1 Isomorphism 4.2 Deletion Subgeometries 4.3 The Imbedding TheoremChapter 5 Theorems of Desargues and Pappus 5.1 Configurations 5.2 Theorem of Desargues 5.3 Theorem of PappusChapter 6 Coordinatization 6.1 Coordinates 6.2 Addition 6.3 Multiplication 6.4 Algebraic Systems and Incidence Bases 6.5 The Coordinatization Theorem 6.6 Finite Projective PlanesChapter 7 Projectivities 7.1 Perspectivities and Projectivities 7.2 Some Classical Theorems 7.3 A Nonpappian ExampleChapter 8 Harmonic Quadruples 8.1 Fano Axiom 8.2 Harmonic QuadruplesChapter 9 The Real Projective Plane 9.1 Separation 9.2 Ordered Fields 9.3 Completeness and the Real Numbers 9.4 Separation for Basis 3.5 9.5 The Real Projective Plane 9.6 Euclidean PlanesChapter 10 Projective Spaces—Part 1 10.1 Axioms for a Projective Space 10.2 ExamplesChapter 11 Projective Spaces—Part 2 11.1 Subspaces and Dimension 11.2 Intervals and Complements 11.3 Dual SpacesAppendix A Hilbert's Axioms for a Euclidean Plane Group I. Axioms of Connection Group II. Axioms of Order Group III. Axiom of Parallels Group IV. Axioms of Congruence Group V. Axiom of ContinuityAppendix B Division RingsAppendix C QuaternionsReferencesIndex of Special SymbolsSubject Index
- Edition: 1
- Published: January 1, 1972
- Imprint: Academic Press
- No. of pages: 232
- Language: English
- Paperback ISBN: 9781483243559
- eBook ISBN: 9781483265209
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