Topic
Crossbar theorem
About: Crossbar theorem is a research topic. Over the lifetime, 1 publications have been published within this topic receiving 2 citations.
Papers
Book•
1 Mar 1999
TL;DR: In this article, the authors present an axiom system for plane geometry: First Steps, Second Steps, Third Steps, Fourth Steps, Fifth Steps, Sixth Steps, Seventh Steps, Eighth Steps.
Abstract: 0. The Question of Parallels. 1. Five Examples. 2. Some Logic. 3. Practice Proofs. 4. Set Terminology and Sets of Real Numbers. 5. An Axiom System for Plane Geometry: First Steps. 6. Betweenness, Segments and Rays. 7. Three Axioms for the Line. 8. The Real Ray Axiom and Its Consequences. 9. Antipodes and Opposite Rays. 10. Separation. 11. Pencils and Angles. 12. The Crossbar Theorem. 13. Side-Angle-Side. 14. Perpendiculars. 15. The Exterior Angle Inequality and Triangle Inequality. 16. Further Results on Triangles. 17. Parallels and the Diameter of the Plane. 18. Angle Sums of Triangles. 19. Parallels and Angle Sums. 20. Concurrence. 21. Circles. 22. Similarity. Appendix I. Definitions and Assumptions from Book I of Euclid's Elements. Appendix II. The Side-Angle-Side Axiom in the Hyperbolic Plane. Bibliography. Index.
2 citations
Performance Metrics
| Year | Papers |
|---|---|
| 1999 | 1 |