What is the opposite of flat? and is it curved?
the tabletop is flat
the tabletop is (not flat or curved).
In other examples could curved be the opposite?
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Curved and flat can be direct antonyms in certain cases, but they usually aren't.
As related to a tabletop, the proper antonym would be uneven, not curved, because tabletops are flat by definition. A curved table would mean that the tabletop is not rectangular or oval in shape, or that it has rounded edges. Something similar to a table but with a vertically curved surface would be a basin or perhaps a bowl or dish.
In mathematics, one can use curved and flat as antonyms for describing the slope or rate of change of the graphs of functions (which are generally called curves). Here's an example on ELU suggesting flat and curved as antonyms in the context of learning curve.
Outside of technical ones, I can't think of any cases where curved and flat are properly used as antonyms.