How many points are there on the globe where, by walking one mile south, one mile east,and one mile north,you reach the place where you started?

Answer:

If you are on north pole, any direction you take is south.
So you walk south, then east back to north makeing equilateral trangle of 1 mile side. Then yes north pole is one point.

Now assume your are 1.159 miles from south pole.
You walk 1 mile towards south. You are 0.159 mile from south pole. by walking 1 mile east (directions on earth are cirular) you would complete full circle 2*Pi*r (r =0.159) = 1 mile and be back at same spot where you started your east walk. Then 1 mile to north. will take you to the same point you started. (1.159, just example, quick thinking, further calculating, you can get, more accurate).

so this is 2nd point.

now 1 + (0.159)/2) from south pole. In this case after walking south for 1 mile, and then east, you wil complete 2 rounds and be at same place where you started your eastward walk. then 1 mile toward north will take you to same point where you sarted.

so this is 3rd pont.

Like this
1 + (0.159)/3 from south pole.. 4th point
1 + (0.159)/4) frrom south pole ..5th point..
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infinity..