Geometry from Euclid to Knots

by Saul Stahl

Overview

Designed to inform readers about the formal development of Euclidean geometry and to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text closely follows Euclid's classic, Elements. The text augments Euclid's statements with appropriate historical commentary and many exercises — more than 1,000 practice exercises provide readers with hands-on experience in solving geometrical problems. In addition to providing a historical perspective on plane geometry, this text covers non-Euclidean geometries, allowing students to cultivate an appreciation of axiomatic systems. Additional topics include circles and regular polygons, projective geometry, symmetries, inversions, knots and links, graphs, surfaces, and informal topology. This republication of a popular text is substantially less expensive than prior editions and offers a new Preface by the author.

Product Details

ISBN-13:	9780486134987
Publisher:	Dover Publications
Publication date:	04/25/2012
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	480
File size:	25 MB
Note:	This product may take a few minutes to download.

About the Author

Saul Stahl

Table of Contents

Preface to the Dover EditionPreface1. Other Geometries: A Computational Introduction2. The Neutral Geometry of the Triangle3. Nonneutral Euclidean Geometry4. Circles and Regular Polygons5. Toward Projective Geometry6. Planar Symmetries7. Inversions8. Symmetry in Space9. Informal Topology10. Graphs11. Surfaces12. Knots and LinksAppendix A: A Brief Introduction to the Geometer's SketchpadAppendix B: Summary of PropositionsAppendix C: George D. Birkhoff's Axiomatization of Euclidean GeometryAppendix D: The University of Chicago School Mathematics Project's Geometrical AxiomsAppendix E: David Hilbert's Axiomization of Euclidean GeometryAppendix F: PermutationsAppendixG: Modular ArithmeticSolutions and Hints to Selected ProblemsBibliographyIndex