Off-topic circumnavigating the earth in a mile or less [was Re: Significant digits in a float?]

[Ethan Furman]

On 04/29/2014 03:51 PM, Chris Angelico wrote:
> On Wed, Apr 30, 2014 at 8:42 AM, emile <emile at fenx.com> wrote:
>> On 04/29/2014 01:16 PM, Adam Funk wrote:
>>
>>> "A man pitches his tent, walks 1 km south, walks 1 km east, kills a
>>> bear, & walks 1 km north, where he's back at his tent.  What color is
>>> the bear?"  ;-)
>>
>>
>>  From how many locations on Earth can someone walk one mile south, one mile
>> east, and one mile north and end up at their starting point?
>
> Any point where the mile east takes you an exact number of times
> around the globe. So, anywhere exactly one mile north of that, which
> is a number of circles not far from the south pole.

It is my contention, completely unbacked by actual research, that if you find such a spot (heading a mile east takes you 
an integral number of times around the pole), that there is not enough Earth left to walk a mile north so that you could 
then turn-around a walk a mile south to get back to such a location.

--
~Ethan~