Description 
xvii, 469 pages : illustrations ; 26 cm. 
Content Type 
text 
Format 
volume 
Series 
Pure and applied undergraduate texts ; 21.

Bibliography 
Includes bibliographical references (pages 451453) 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) nonEuclidean 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.


Geometry.

ISBN 
9780821884782 (alk. paper) 

0821884786 (alk. paper) 
Standard # 
40022448983 
OCLC number 
821066968 
