Euclidean and Riemannian Geometry

Abstract

Euclidean geometry can be understood as a theory that derives from the construction of its fundamental concepts and whose theorems are true on the basis of its evident clarity [Evidenz]. The theorems of Euclidean geometry are therefore strictly valid for all objects of experience. On the other hand, the general theory of relativity shows that for the proportions of empirical objects it is not the Euclidean, but the Riemannian geometry which is valid.The question therefore arises how these two apparently contradictory assertions can be reconciled. To answer this question, the basis for the evident clarity of Euclidean geometry as well as the empirical-physical arguments for the theory of relativity must be considered.KeywordsMass PointRiemannian GeometryEuclidean GeometryRiemannian SpaceEmpirical RealizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.