Axiomatic geometry
 Responsibility
 John M. Lee.
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2013]
 Physical description
 xvii, 469 pages ; 26 cm.
 Series
 Pure and applied undergraduate texts ; volume 21.
Access
Creators/Contributors
 Author/Creator
 Lee, John M., 1950
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Euclid Incidence geometry Axioms for plane geometry Angles Triangles Models of neutral geometry Perpendicular and parallel lines Polygons Quadrilaterals The Euclidean parallel postulate Area Similarity Right triangles Circles Circumference and circular area Compass and straightedge constructions The parallel postulate revisited Introduction to hyperbolic geometry Parallel lines in hyperbolic geometry Epilogue: Where do we go from here? Hilbert's axioms Birkhoff's postulates The SMSG postulates The postulates used in this book The language of mathematics Proofs Sets and functions Properties of the real numbers Rigid motions: Another approach References Index.
 (source: Nielsen Book Data)
 Publisher's 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 model 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Pure and applied undergraduate texts ; volume 21
 ISBN
 9780821884782 (alk. paper)
 0821884786 (alk. paper)