Geometry
From Euclid to Knots
Published on 10. January 2003
Book
Hardback
458 pages
978-0-13-032927-1 (ISBN)
Description
For Junior-level courses in Geometry.
Designed to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text augments Euclid's elegant but sparse statements with appropriate historical commentary and many exercises. It also introduces the non-Euclidean geometries, allowing students to gain perspective and enhance their appreciation of axiomatic systems.
Designed to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text augments Euclid's elegant but sparse statements with appropriate historical commentary and many exercises. It also introduces the non-Euclidean geometries, allowing students to gain perspective and enhance their appreciation of axiomatic systems.
More details
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 240 mm
Width: 182 mm
Thickness: 21 mm
Weight
864 gr
ISBN-13
978-0-13-032927-1 (9780130329271)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
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.
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.