Study on the Approach to Realize the Thought of Gauss' Non-Euclidean Geometry

The thought of Gauss' non-Euclidean geometry is intended to reveal that the Euclidean geometry does not have the only physics necessity.Gauss' intrinsic differential geometry,however,has deeply revealed the non-Euclidean nature of geometry spaces.This paper studies the inherent relations between Gauss' intrinsic differential geometry and non-Euclidean geometry,and the approach to realize his non-Euclidean geometry,and the authentication of his non-Euclidean geometry in his actual geodesy.This paper points out that the thought of Gauss' intrinsic differential geometry has pointed out a differential geometry approach of the development and confirmation of non-Euclidean geometry.