A person on the surface of earth moves one km south one km west and one km north and reach the same initial position
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If you are at the North Pole you will walk south then west then north and windup where you started because the third leg of your journey sends you towards the pole by definition tracing out a polar triangle shape.
If you are at the South Pole, you ain't goin’ nowhere. (Excuse my grammar). You stay at the Pole because you cannot walk south from the South Pole. You could only walk North on the first leg of any journey.
If you are at any place on the Earth besides the poles, the answer varies based on your starting point. If you straddle the equator by starting 1/2 mile north of the equator, you trace out three sides of a polar quadrangle. You windup exactly one mile west of your original this case only.
If you start out within one mile of the South Pole, you will cross the South Pole before you can walk a mile. If you crossed the South Pole, you would be walking North, no longer South, so it is impossible to walk a mile South unless you start full mile North of the North Pole. However if you are at the South Pole at the end of the first segment, it is impossible to walk West one mile on the second segment of the journey b cause you are on the pole; another impossible assignment.
Near the South Pole you could walk West on the second segment only of you are at more than 1/2 PI miles North of the South Pole at your starting point. However, your second segment would be a full circle followed by a third segment that retraces the first segment winding you up where you started. If you start out closer than 1/2 PI miles from the South Pole, the closer you start towards the Pole, but greater than one mile, your second segment is more than one full circular walk around the pole and those trips are just too complex to pursue any further here. Too many circular walks to reach one mile on the second segment the closer to one mile from the South Pole your starting point is. (but greater than one mile from the Pole)
If you are at the South Pole, you ain't goin’ nowhere. (Excuse my grammar). You stay at the Pole because you cannot walk south from the South Pole. You could only walk North on the first leg of any journey.
If you are at any place on the Earth besides the poles, the answer varies based on your starting point. If you straddle the equator by starting 1/2 mile north of the equator, you trace out three sides of a polar quadrangle. You windup exactly one mile west of your original this case only.
If you start out within one mile of the South Pole, you will cross the South Pole before you can walk a mile. If you crossed the South Pole, you would be walking North, no longer South, so it is impossible to walk a mile South unless you start full mile North of the North Pole. However if you are at the South Pole at the end of the first segment, it is impossible to walk West one mile on the second segment of the journey b cause you are on the pole; another impossible assignment.
Near the South Pole you could walk West on the second segment only of you are at more than 1/2 PI miles North of the South Pole at your starting point. However, your second segment would be a full circle followed by a third segment that retraces the first segment winding you up where you started. If you start out closer than 1/2 PI miles from the South Pole, the closer you start towards the Pole, but greater than one mile, your second segment is more than one full circular walk around the pole and those trips are just too complex to pursue any further here. Too many circular walks to reach one mile on the second segment the closer to one mile from the South Pole your starting point is. (but greater than one mile from the Pole)
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