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If you travel north or south a significant distance, you will see a different set of stars at night. This will not happen on a flat surface.
During lunar eclipses, the projected shadow of the earth on the moon is always round. If the earth were flat, then this projection will not always be circular (it could degenerate to a line!). But this is never observed, regardless of the time of the lunar eclipse.
If you look out the window on a trans-Atlantic flight, you can, most of the times, see the curvature of the earth in the horizon.
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