Another spherical problem

Acolyte
Posers and Puzzles 18 Jun '04 21:24
1. Acolyte
18 Jun '04 21:24
Suppose the Earth is a perfect sphere (of unit radius). Starting somewhere other than the poles, you travel in a zigzag, where you start by travelling in a straight line which is initially due west, then turn round and go on a path which is initially due east, and so on. You make infinitely many turns, but the total distance you travel is finite. Under what conditions will you end up on the equator?
2. royalchicken
CHAOS GHOST!!!
18 Jun '04 22:16
Originally posted by Acolyte
Suppose the Earth is a perfect sphere (of unit radius). Starting somewhere other than the poles, you travel in a zigzag, where you start by travelling in a straight line which is initially due west, then turn round and go on a path which is initially due east, and so on. You make infinitely many turns, but the total distance you travel is finite. Under what conditions will you end up on the equator?
Wait, how far around do I turn? If I'm initially heading west, do I then turn in the opposite direction and go back the way I came (east) or do I go east from the way I am currently facing (ie north from the point of view that defined west in my first walk)?
3. Otis
Lucky Patzer
18 Jun '04 23:43
Directions don't change, besides you'll fall of the Earth if you go too far
4. Acolyte