Logicians who study non-Euclidean geometries discovered something interesting: It is often possible to find Non-euclidean geometries on surfaces in Euclidean Geometries. One can fine Euclidean Geometries on non-Euclidean surfaces.

Noteably, architects can use a Cartesian Plane to design and construct buildings on planet earth despite the fact that the surface of the Earth does not conform to a flat plane.

Riemann Geometry is largely based on the exploration of these different types of logical surfaces.

I suspect that many of the games people play with flat earth claims are based on this observation.

Historians of science like to focus on how the Heliocentric Model of the solar system replaced the Ptolemaic System.

Most people forget that the Ptolemaic Model, with its bizarre epicycles, is still mathematically correct.

Galileo originally argued for a heliocentric model in which the planets had circular orbits. The Ptolemaic Model did a better jobs describing the positions of the stars than this circular model.

Ptolemy held that the earth was a sphere. Ptolemy did a better job measuring the circumference of the earth than the French.

When exploring these different models is fun to put forward different cosmological view.

The thing I hate about the flat-earthers is that take the wonderful models that one can use different mathematical models to describe the same thing and turn it into an ugly ideological battle.

They are more interested in the dialectical argument than on conciliatory path which sees values in different models. The Flat-earthers are pretty good at triggering a response.

People who love arguing for the sake of arguing end up hurting anyone who gets trapped in their arguments.