There are some points on Earth for which the following is true:
Starting from one of these points, you can walk 1 km South, then 1 km East, then 1 km North, and you will wind up back where you started from.
One such point is the North Pole. Where are others?
There are an infinite number of corret answers. There is a circle created by all points that are (1+(1/(2*pi))) km away from the South Pole. If you start at any point on the circle, you walk south 1 km, then walk east 1 km (A perfect circle around the south pole, which brings you back where you started walking east). You walk north 1 km and end up back at the original starting point.
As TomM said, you can also pick a starting point where walking east 1 km causes you to make two complete circles around the south pole and end up in the same spot where you were when you started circling the south pole. The same goes for circling the south pole 3 time, 4 times, 5 times, etc. For n equals all whole numbers, you can start anywahere that is (1+(1/(2*pi*n))) km from the South Pole.
TomM's answer in mathmatical terms
