Assume for this problem that the earth is a perfect sphere. A point \(P\) on it's surface has the following property. Starting from \(P\), suppose you travel \(1\) mile south, then \(1\) mile west and finally \(1\) mile north. Doing so takes you back to the same point \(P\). Are there any such points \(P\) other than the north pole? Choose the appropriate option:
There are no such points.
Such points for a single circle.
Such points form at least two but finitely many circles.
Such points form infinitely many distinct circles.