7 THE EARTH AND AN EIGENVALUE

Two contestants are each given an inflatable globe. They are asked to place the globe on the floor. The globe may be in any rotation that they choose. Once they have placed the globes, the goal is to find a spot on the globe, such as a city, that has the same position on both globes. Being in the same position means that if 2 tiny people would stand on that place on each of the inflatable globes and would point a laser pointer into the sky, perpendicular to the surface, the 2 laser beams would be parallel. The place can be anywhere on the globe, and it can be a city, a point in a desert, or in the ocean. As an example, if both contestants chose to place the South Pole on the floor, then the North Pole would be such a point: on both globes, it points vertically into the sky (the South Pole would be another correct answer, of course). But the contestants can choose any rotation, so in general, the correct point does not need to be the North Pole, and it does not need to point vertically upward. The figure below shows another example.