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Walking around the world?

Assume for this problem that the earth is a perfect sphere. A point \(P\) on it's surface has the following property. Starting from \(P\), suppose you travel \(1\) mile south, then \(1\) mile west and finally \(1\) mile north. Doing so takes you back to the same point \(P\). Are there any such points \(P\) 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.

Note by Paramjit Singh
3 years, 10 months ago

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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.

Michael Mendrin - 3 years, 10 months ago

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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.

Michael Mendrin - 3 years, 10 months ago

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Can you clarify what you mean by "making n number of circuits"?

Paramjit Singh - 3 years, 10 months ago

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There are no such points.

Sarveshwar Kasarla - 3 years, 10 months ago

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No. Check your reasoning.

Paramjit Singh - 3 years, 10 months ago

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