Roads to Geometry

This new book clarifies, extends, and unifies concepts discussed in basic high school geometry courses. It gives readers a comprehensive introduction to plane geometry in a historical context. Chapter topics include axiomatic systems, axiom sets for geometry, neutral geometry, Euclidean geometry of the plane, analytic and transformational geometry, non-Euclidean geometries, and projective geometry. For anyone in need of a refresher course in geometry.

1. Rules of the Road: Axiomatic Systems.
2. Many Ways to Go: Axiom Sets for Geometry.
3. Travelling Together: Neutral Geometry.
4. One Way to Go: Euclidean Geometry of the Plane.
5. Side Trips; Analytic and Transformational Geometry.
6. Other Ways to Go: Non-Euclidean Geometries.
7. All Roads Lead to: Projective Geometry.
Appendix A: Euclid's Definitions and Postulates, Book 1.
Appendix B: Hilbert's Axioms for Euclidean Plane Geometry.
Appendix C: Birkhoff's Postulates for Euclidean Plane Geometry.
Appendix D: The SMSG Postulates for Euclidean Geometry.
Appendix E: Exploratory Lab Activities to Supplement Exercise Sets in Chapters 4, 5, and 6.

What is included with this book?

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Table of Contents

Supplemental Materials