Fun logic problem 4: walking the earth and ending up where you started

Question

there are places on earth, where, you can walk 1 mile south, one mile east, and 1 mile north and end up where you started. One solution is exactly at the north pole. Find all the other places where this could be true.

Answer 1

If you were about 1.16 miles from the South Pole, you could walk 1 mile south, then one mile east with would cause you to make a circuit of the South Pole then one mile north and you would be back where you started.

Great problem btw.  I had to think about it.  

(edit) to be a bit more precise, you should start out 1 + 1/2pi miles from the south pole.

(edit) ok - I though of some more.  If you were a distance of one mile plus 1/(2 * n * pi) miles from the South Pole (where n is an integer), you could walk a mile south then walk east circling the pole n times then return to your original location.