Assume for this problem that the earth is a perfect sphere. A point on it's surface has the following property. Starting from , suppose you travel mile south, then mile west and finally mile north. Doing so takes you back to the same point . Are there any such points other than the north pole? Choose the appropriate option:
There are no such points.
Such points for a single circle.
Such points form at least two but finitely many circles.
Such points form infinitely many distinct circles.
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"Such points can form infinitely many distinct circles", because one can start at a point that is 1 + x miles from the South pole, travel 1 mile south to a distance x from the South Pole, such that in travelling west 1 mile one can end up making n number of circuits coming back to exactly where one was before travelling west, and thence travel 1 mile north back to the point of beginning P. n can be any integer.
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Can you clarify what you mean by "making n number of circuits"?
x = 1 / 2πn, where n is any integer > 0. Then n circuits or trips around will bring him back to the point where he began traveling west.
There are no such points.
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No. Check your reasoning.