one mile south
Regarding the posted solution for the 'one mile south'... considering the circle of locations, it's pretty clear to me that it indeed exists. My reasoning:
Well, clearly there is a parallel near the south pole whose circumference is 1 mile -- since the equator is a lot loner than one mile, and the circumference of parallels steadily goes down to zero as you approach the pole.
Also (somewhat less clearly, but still), you can go one mile north from any point on the one-mile parallel; this is true because the one-mile parallel is ways away from the equator, so there is plenty of room to go north. If you had a teeny planet where the one-mile parallel were very close to the equator, then you couldn't go one mile north from there.
Finally, even that's not all the solutions. You can also be one mile north from the 1/2-mile parallel, or the 1/3 mile parallel, or any 1/n parallel, where n is a positive integer.
Tuesday, June 03, 2003
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