Questions for a Sphere

(notes by John Munchak)

1. What is a sphere? How shall we define it? (Will we include words like center, radius?) Can we think of it as a “surface of revolution of a circle about an axis?”
2. What is volume?
3. What is surface area?
4. How do we define the distance between two points? Will it be the shortest path along the surface?
5. How do we measure an angle?
6. What is a segment?
7. What is a triangle? How many degrees does a triangle have?
8. What is a line?
9. What is parallel? What is perpendicular?
10. What is a circle?
11. What are cross sections?
12. How do we perform a reflection?
13. What objects do we get with certain intersections – a sphere with: a line, a plane, another sphere?
14. How large are these objects?
15. How do I get the “biggest circle” or the “great circle?”
16. How do we get the shortest path or “Great Circle Route?”
17. How do we define symmetry?
18. How do we put a tessellation on a sphere (like a soccer ball)?
19. What distortions occur when projecting a sphere (like a map)?
20. What does “straight” mean?
21. How are cylinders and cones related to spheres?