The question is this:
> I go south one mile, east one mile, north one mile, and end up where I started.

The usual answer is the north pole. But the thing is, that **there are infinitely
many points with this property, all but one of which are near the south pole**.

To see this, here is a picture:

![]{centre shadow}(Circum1.jpg) 

If we start at a point \(P_0\) which is exactly \(1+\frac{1}{2\pi}\) miles from the south pole,
and walk one mile south, we find ourselves at a point \(P_1\) exactly \(\frac{1}{2\pi}\) miles from the
south pole. If we then go east one mile, we complete a whole circle of radius \(\frac{1}{2\pi}\),
so end up at \(P_1\) again. If we then go a mile north, we get back to \(P_0\).

Indeed, if we start at a point exactly \(1+\frac{1}{2n\pi}\) miles from the south pole, for
any positive integer \(n\), we will also end up exactly where we started.

*Image made with [Blender](https://www.blender.org/). Earth texture came [from here](https://www.solarsystemscope.com/textures/)*