The other places are just slightly further north than "one mile north of south".
The distance around the world is about 26,000 miles at the equator, reducing as you move to the north or south poles, and zero at the poles. There must be a point near the south pole where the distance around the world is one mile exactly. Start one mile north of here. There must also be a place where the distance around the world is half a mile. Start one mile north of here. And so on.