Euclidean geometry is two-dimensional in plane geometry, while Roche geometry is almost a geometric proposition that does not involve parallel axioms. If it is correct in Euclidean geometry, it is also correct in hyperbolic geometry. However, the proposition that depends on parallel axioms is not valid in hyperbolic geometry. Riemannian geometry is different from plane geometry. It is applied to surfaces and involves calculus. . . He first developed the concept of space, and proposed that the object of geometry research should be a multiple generalized quantity, and the points in space can be described by n real numbers (x 1, ..., xn) as coordinates. This is the original form of modern N-dimensional differential manifold, which lays the foundation for describing natural phenomena in abstract space.