In Experiencing Geometry on Plane and Sphere, Henderson invites readers to explore the basic ideas of geometry beyond the formulation of proofs. The text conveys a distinctive approach, stimulating readers to develop a broader, deeper understanding of mathematics through active participation—including discovering, discussing and writing about fundamental ideas. It provides a series of interesting, challenging problems, then encourages readers to gather their reasonings and understandings of each problem and discuss their findings in an open forum.
1. Straightness and Symmetry. 2. "Straightness" on a Sphere. 3. What is an Angle? 4. Straightness on Cylinder and Cone. 5. SAS and ASA. 6. Area, Parallel Transport and Holonomy. 7. ITT, SSS and ASS. 8. Parallel Transport. 9. SAA and AAA. 10. Parallel Postulates. 11. 3-Spheres in 4-Space. 12. Dissection Theory. 13. Square Roots, Pythagoras and Similar Thoughts. 14. Geometric Solutions of Quadratic and Cubic Equations. 15. Projections of a Sphereonto a Plane. 16. Duality and Trigonometry. 17. Isometries and Patterns. 18. Polyhedra. Appendix A. A Geometric Introduction to Differential Geometry. Bibliography. Index.