[Alamo-Girl]

Er, I thought Euclidean Geometry is the study of flat space whereas Riemannian Geometry is the study of curved and higher dimensional space.

[Physicist]

Er, I thought Euclidean Geometry is the study of flat space whereas Riemannian Geometry is the study of curved and higher dimensional space.

Right, but the real world is curved and higher-dimensional. Of course, Euclid works as a splendid approximation, and hence is useful, but if you're talking in absolute physical terms about "true" vs. "false"...

Now, who's going to be the one to bring up the issue of provability? :-)