Chapter 7.6, Problem 36MS

The Earth moved (ExH). Consider a transformation of the sphere that consists of moving each point by shifting its longitude by ${30}^{\circ }$ to the west and by increasing its latitude by squeezing points upward away from the south pole and toward the north pole. This process keeps the north and south poles fixed and spirals points upward toward the north pole and away from the south pole. Describe the movement of the equator under the first two iterations of this process. What points are fixed under this transformation?