Answer to the question: There are infinite points, all within about 1.2 miles 
from the south pole.
 
The furthest from south pole is a circle, with the latitude equals (in radians)

-Cos-1(1/2πR) + 1/R

Where R is the radius of the earth.

 

If one is allowed to go more than one loops (N), we get infinite number of 
circles, with the latitude equals

-Cos-1(1/2πNR) + 1/R, N=2, 3, ..., to infinity

 

When N -> infinity, it is any place 1 mile north of the south pole. 

 
 

 
** 

 

Which brings up the question: The North Pole is one place on a globe where you 
can walk one mile south, one mile east and one mile north and return to your 
point of origin. Name another.


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