Axiomatic Geometry - Mathematics 360 - Spring 2009

For Homework 6

1. Using stereographic projection, what transformation of the sphere does the rotation of the complex plane by 90 degrees about the origin lift to? Prove your answer algebraically.
2. Using stereographic projection, what transformation of the sphere does the rotation of the complex plane by theta degrees about the origin lift to?  Prove your answer algebraically.
3. Using stereographic projection, what transformation of the sphere does a stretching of the complex plane from the origin lift to? Just describe it in words or pictorially. Algebraic proof is not necessary.
4. Using stereographic projection, what transformation of the sphere does a horizontal translation of the complex plane lift to? Just describe it in words or pictorially. Algebraic proof is not necessary.