1. Rotations
2. Let R be a rotation by 0 < < 360 degrees around a point O on E² or H².
3. Prove that O is the only fixed point of R, that is, the only point that R takes to itself.
4. Warning: 180 degrees is a special case.
5. What happens on S²? Be as explicit as possible.
6. Why doesn't your proof from part (a) work here?

E² = Euclidean Plane

H² = Hyperbolic Plane

S^{2= Sphere}