Sorry, wasn't quite clear. I was thinking of circles and squares in the system of Euclidean geometry, where we could present well-defined definitions and deductions, rather than as physical approximations to these concepts in a non-Euclidean universe.

Time for a joke: What's the difference between an engineer, a physicists, and a mathematician?

The engineer thinks his equations are approximations of the real world.
The physicists thinks the real world is an approximation of his equations.
And the mathematician hasn't spotted the connection yet!

C'est drôle parce que c'est vrai!