EXPERIENCING GEOMETRY
ON PLANE AND SPHERE

Contents:

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 Triangles

14. Geometric Solutions of Quadratic and Cubic Equations

15. Projection of a Sphere onto a Plane

16. Duality and Trigonometry

17. Isometries and Patterns

18. Polyhedra

Appendix: A Geometric Introduction to Differential Geometry