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I have a very faint idea of General Relativity.. hence this question. I think that according to General Relativity, the shortest distance between two points on this Earth is along a curved path, which is the curvature of the Earth [or sorta.. parallel to it]. Hence, i assumed that when on earth, we measure an area of the land, and we treat it as a rectangle, we are not making an approximation, but that, in fact is the actual area we calculate on this earth.

so, is it true that if we are to measure the surface area of the Earth while being on the earth, we will measure it to be [itex]4\pi^2 R_e^2[/itex] rather than [itex]4\pi R_e^2[/itex]??

so, is it true that if we are to measure the surface area of the Earth while being on the earth, we will measure it to be [itex]4\pi^2 R_e^2[/itex] rather than [itex]4\pi R_e^2[/itex]??

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