On Wed, Apr 30, 2014 at 11:14 PM, Ethan Furman <et...@stoneleaf.us> wrote: >> 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.
The circle where the distance is exactly one mile will be fairly near the south pole. There should be plenty of planet a mile to the north of that. If the earth were a perfect sphere, the place we're looking for is the place where cutting across the sphere is 1/π miles. The radius of the earth is approximately 4000 miles (give or take). So we're looking for the place where the chord across a radius 4000 circle is 1/π; that means the triangle formed by a radius of the earth and half of 1/π and an unknown side (the distance from the centre of the earth to the point where the chord meets it - a smidge less than 4000, but the exact distance is immaterial) is a right triangle. Trig functions to the rescue! We want latitude 90°-(asin 1/8000π). It's practically at the south pole: 89.9977° south (89°59'52"). Are my calculations correct? ChrisA -- https://mail.python.org/mailman/listinfo/python-list
