Welcome to online math forum,
The application of math to the real world is based on induction: we
try something repeatedly and see that, yes, our calculations about
circumference do work in the real world, so the assumptions on which
they are based must be accurate.
If we measured big enough circles, we
would find that relativity makes it not quite work right; math help; that means
that the world doesn't quite match the Euclidean geometry on which our
calculations are based. But induction does show us that it is a close
enough approximation in normal cases.
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