California State University, Northridge WordmarkOviatt Library WordmarkOviatt Library Catalog Wordmark
Author Lee, John M., 1950-
Title Axiomatic geometry / John M. Lee.
Published Providence, Rhode Island : American Mathematical Society, [2013]
Book Cover

 Floor4  QA481 .L44 2013    IN LIBRARY
Description xvii, 469 pages : illustrations ; 26 cm.
Content Type text
Format volume
Series Pure and applied undergraduate texts ; 21
Pure and applied undergraduate texts ; 21.
Bibliography Includes bibliographical references (pages 451-453) and index.
Contents 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.
Summary 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.
Subject Axioms.
ISBN 9780821884782 (alk. paper)
0821884786 (alk. paper)
Standard # 40022448983
OCLC number 821066968