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The curvature of a ringworld is so slight from the vantage point of someone standing on the surface that it would be unnoticeable. The "land" would seem to go off into infinity as a "flatland" until atmospheric haze obscured it from view at sufficient distances.
Think of the curvature of the surface of the Earth (and the horizon we perceive from the surface) , and compare that to the curvature of an immense ringworld along its entire orbital arc.