In special relativity Einstein used Pythagorean theorem for proving Lorenz transformations. But in general relativity we discovered that space-time has curvature near massive objects, so the geometry near them isn't euclidean. The question is, how can we use Pythagorean theorem in special relativity, if general relativity proves that geometry in our world isn't fully Euclidean ? Or am I missing something?
Sorry made a mistake, they were right, specialty could handle some acceleration. I put some thought and the main debates here was about the Pythagorean theorem. Actually, the space in both GR and SR was assumed to be manifold, of which obay local euclidean geometry, and Pythagorean theorem holds on euclidean space. Even in curved space, the differential form of Pythagorean theorem holds i.e. $ds^2=dx^2+dy^2+dz^2$(only 3 space), which was essentially how they calculated the expression through Pythagorean in SR. Quote Ben's "negligible on sufficiently short distance scales", in infinitesimal, they were "equal".