If you walked one mile south one mile westand then one mile northand ended up where you started where would you be?

Answer 1

There are an infinite number of places you could be.

The usual answer to this question is that you are at the North Pole. When you walk south you are one mile away from the pole. Then when you walk west you are walking in an arc around the pole. Then when you walk north you are back at the North Pole.

However, you could also be in a number of places near the South Pole. From the North Pole answer we see that when we walk west that we are walking in an arc relative to the pole. If we continue to walk west, we will eventually end up back at place where we started walking west, after we have walked a complete circle. Now consider that near the South Pole we can trace a circle that has a circumference of 1 mile. Once you have defined that circle, then we can start our journey at any of the "infinite" points that are 1 mile north of that circle. In this case we would walk south 1 mile, then walk west one mile, exactly circling the South Pole, and finally walk north 1 mile, returning to where we started.

A: Milton Keynes - it happened to me once!