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" Axiomatic geometry / "
John M. Lee.
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BL
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| Record Number
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846972
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| Main Entry
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Lee, John M.,1950-
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| Title & Author
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Axiomatic geometry /\ John M. Lee.
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| Publication Statement
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Providence, Rhode Island :: American Mathematical Society,, [2013]
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, ©2013
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| Series Statement
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Pure and applied undergraduate texts ;; 21
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| Page. NO
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xvii, 469 pages :: illustrations ;; 26 cm.
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| ISBN
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0821884786
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: 9780821884782
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| Bibliographies/Indexes
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Includes bibliographical references (pages 451-453) and index.
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| Contents
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1. Euclid -- 2. Incidence geometry -- 3. Axioms for plane geometry -- 4. Angles -- 5. Triangles -- 6. Models of neutral geometry -- 7. Perpendicular and parallel lines -- 8. Polygons -- 9. Quadrilaterals -- 10. The Euclidean parallel postulate -- 11. Area -- 12. Similarity -- 13. Right triangles -- 14. Circles -- 15. Circumference and circular area -- 16. Compass and straightedge constructions -- 17. The parallel postulate revisited -- 18. Introduction to hyperbolic geometry -- 19. Parallel lines in Hyperbolic geometry -- 20. Epilogue: Where do we go from here? -- Appendices.
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| Abstract
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The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.
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| Subject
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Axioms.
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| Subject
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Geometry.
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Axiomatik.
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Axioms.
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Geometrie.
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Geometry-- Instructional exposition (textbooks, tutorial papers, etc.)
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Geometry-- Real and complex geometry-- Euclidean geometries (general) and generalizations.
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Geometry-- Real and complex geometry-- Hyperbolic and elliptic geometries (general) and generalizations.
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Geometry.
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| Dewey Classification
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516
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| LC Classification
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QA481.L44 2013
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| NLM classification
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51-0151M0551M10msc
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