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If a person stands on the north, or south pole. How do they determine which way is east/west?
No matter where you are on earth direction is determined based on one other point, which is the point opposite it. When you're at the North Pole your opposite point (antipode) is the South Pole.
As soon as you move away from the exact North Pole this changes - on the earth we determine east/west (perpendicular to the North/South Poles) based on the rotation of the earth around its' axis.
This is the theory at least - in practice this can be a bit trickier since the earth is not a perfect sphere.
If we consider North Pole as infinitesimally small point then when you stand such that rotational axis passes through your body center, and start rotating counter-clockwise then parts of your body outside the axis would be moving east.