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Geometry : From Euclid to Knots

Geometry : From Euclid to Knots - 03 edition

Geometry : From Euclid to Knots - 03 edition

ISBN13: 9780130329271

ISBN10: 0130329274

Geometry : From Euclid to Knots by Saul Stahl - ISBN 9780130329271
Edition: 03
Copyright: 2003
Publisher: Prentice Hall, Inc.
Published: 2003
International: No
Geometry : From Euclid to Knots by Saul Stahl - ISBN 9780130329271

ISBN13: 9780130329271

ISBN10: 0130329274

Edition: 03

Summary

The main purpose of this book is to inform the reader about the formal, or axiomatic, development of Euclidean geometry. It follows Euclid's classic text Elements very closely, with an excellent organization of the subject matter, and over 1,000 practice exercises provide the reader with hands-on experience in solving geometrical problems. Providing a historical perspective about the study of plane geometry, this book covers such topics as other geometries, the neutral geometry of the triangle, non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, graphs, surfaces, and knots and links.

Table of Contents

Table of Contents

1. Other Geometries: A Computational Introduction.
2. The Neutral Geometry of the Triangle.
3. Nonneutral Euclidean Geometry.
4. Circles and Regular Polygons.
5. Toward Projective Geometry.
6. Planar Symmetries.
7. Inversions.
8. Symmetry in Space.
9. Informal Topology.
10. Graphs.
11. Surfaces.
12. Knots and Links.


Appendix A: A Brief Introduction to The Geometer's Sketchpad.
Appendix B: Summary of Propositions.
Appendix C: George D. Birkhoff's Axiomatization of Euclidean Geometry.
Appendix D: The University of Chicago School Mathematics Project's Geometrical Axioms.
Appendix E: David Hilbert's Axiomatization of Euclidean Geometry.
Appendix F: Permutations.
Appendix G: Modular Arithmetic.
Solutions and Hints to Selected Problems.
Bibliography.