Geometry from Euclid to Knots [NOOK Book]

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 ...
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Geometry from Euclid to Knots

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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.
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Product Details

  • ISBN-13: 9780486134987
  • Publisher: Dover Publications
  • Publication date: 4/25/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 480
  • File size: 24 MB
  • Note: This product may take a few minutes to download.

Table of Contents


Preface to the Dover Edition
Preface
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 Axiomization of Euclidean Geometry
Appendix F: Permutations
AppendixG: Modular Arithmetic
Solutions and Hints to Selected Problems
Bibliography
Index
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