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# An old riddle - rexamined (Einstein)

## Question

An old riddle runs as follows.  An explorer walks one mile due south, turns and walks one mile due east, turns again and walks one mile due north.  He finds himself back where he started.  He shoots a bear.  What color is the bear? The time-honored answer is: "White," because the explorer musty have started at the North Pole.  But not long ago someone made the discovery that the North Pole is not the only starting point that satisfies the given conditions!  Where else can someone walk a mile south, a mile, east, a mile north and find himself back at his original location?

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Maybe...

Anywhere that is exactly 1 mile from the South Pole. 1 mile south to the pole 1 mile "east" which doesn't exist then back north to your original spot.

And...

Anywhere a mile north of where the earth has a circumference of exactly 1 mile.

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And

Anywhere a mile north of where a circle of constant latitude has a circumference of 1/n miles, n=2, 3, ...

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Actually, there are many places like that.

"one mile due east" does not imply the length of the parallel being one mile, it can be half a mile, 1/3 mile, 1/4 mile ... 1/n mile.

In theory, infinity.

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