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?

In normal scenario if you think immediate answer will be zero as moving above directions will form 3 sides of a square. But here is the trick. Answer is not zero.
But precisely at north pole every direction is south only. At this point walking south one mile will place u at 1 mile to the south. For there if u walk east then you will form a circlular path centered at north pole. from there if you walk 1 mile north then again you will reach the point where you started. This journey looks like a wedge of pie. Samething holds good at south pole. But here you need to start little more than 1 mile away from south pole as you cannot go to south from the south pole. Then from this point u go 1 mile south. There walk east to form a full circle of 1 mile circumference and then walk 1 mile north. You will reach where u started. on circumference you can do this on infinite number of points. Similarly you can start little bit away from pole from where if you walk closer to pole one mile you will form a circle of circumference 1/2 mile(2 revolutions while walking east), 1/3 mile etc.....
So there are infinite number of points where you can do this.