Many of you don't know this, but as a young man, Greg once decided to worship the moon. He was so obsessed by the moon that he once decided to start following it. So at any given moment, he would check where the moon is and then walk in that direction. Greg has special powers so that he can see the moon always, even when it's "beneath the earth". Also, Greg can walk with a constant speed (much less than the moon of course) without ever resting. He can also walk over water, etc. The question to you is: where did Greg end up? Try to find an attractive mathematical model that descibes this situation but isn't too complicated. Then figure out what happens to Greg's walking path asymptotically. Is this dependent of where Greg starts? Prove it!