### 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?

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..
.
.
.
.

infinity..

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