No, the Earth is not flat
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Different constellations are seen from different places on Earth
Certain constellations can only be seen in the Northern Hemisphere but disappear in the Southern Hemisphere. The vice-versa is true as well. The Earth is a globe because constellations appear to shift and disappear due to the spherical curvature of the Earth.
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The north star (Polaris) cannot be seen farther than about 2° south latitude. Using FE measurements (12,500 miles from the north pole to the ice wall or dome, 3,100 mile Polaris altitude), neither pole star (Polaris/Sigma Octantis) should ever be visibly lower than 14° above the horizon. Greek philosopher Aristotle also figured out in 350 B.C. that different constellations are visible from different latitudes. For example, the Big Dipper is always visible at 41° north latitude, but below 25° south latitude, it can't be seen at all. On the other hand, in the Southern Hemisphere, the Southern Cross can't be seen until south of Florida Keys in the Northern Hemisphere. Since different constellations are seen in different places, the Earth is a globe.
The sun, moon, and stars are all objects only a few thousand miles above the sea level of the Earth. As a result, all of these objects are very small. The reason why constellations only appear in certain parts of the world is because of the effect of perspective. For example, with the Big Dipper, the constellation cannot be seen in the Southern Hemisphere because of the increased distance between where one is standing and the constellation.
[P1] Stars and constellations are only visible in certain parts of the world, meaning that the Earth is a globe.
Rejecting the premises
[Rejecting P1] Stars and constellations are only visible in certain parts of the flat world because the farther you walk away from them, the smaller they appear, until they disappear altogether.