PDC and a Nice Geographic Puzzle

Hi Folks,

At PDC I gave a talk largely inspired by topics raised here and in the spatial forums.  But “inspired by” doesn’t equate to “a duplicate of”, and to turn things around, I’ve been meaning to write a few posts here inspired by my PDC talk.  Stay tuned.

In the meantime, Rob Mount from Intergraph sent me a note that started:

As I review your PDC presentation I’m reminded of a puzzle I think you’ll enjoy. 

I did indeed, and I hope a lot of you will enjoy it as well.  Rob started out with a puzzle I expect most of us have heard before:

When I was growing up one of my uncles was fond of challenging the children in the family with puzzles.  One of my favorites, as a very young child, was this one: A hunter walks a mile south, a mile east and a mile north and finds himself back at the starting point.  A bear walks by.  What color is the bear?

This is well-known enough that I don’t think the answer will be much of a spoiler:

He, of course, thought the hunter started at the North Pole.  The bear was a polar bear and hence white.

A perfectly valid answer, of course.  But Rob continues:

Years later I finally got my revenge by stumping him with this problem:  I reminded him of the hunter and the polar bear and pointed out that there are actually several other points on the earth that meet the geographic constraint he stated – if you walk a mile south, a mile east and a mile north you find yourself back where you started.

Assuming a spherical earth, how many such points exist and where are they?

I won’t spoil this one so quickly.  Go ahead and post your answers in the comments; I’ll post the solution in a few days.