3、英文维基原话:（1）Classical Greek geometry defined the Euclidean plane and Euclidean three-dimensional space using certain postulates, while the other properties of these spaces were deduced as theorems. Geometric constructions were also used to define rational numbers as ratios of commensurable lengths. When algebra and mathematical analysis became developed enough, this relation reversed and now it is more common to define Euclidean spaces from vector spaces, which allows using Cartesian coordinates and the power of algebra and calculus. This means that points are specified with tuples of real numbers, called coordinate vectors, and geometric shapes are defined by equations and inequalities relating these coordinates. This approach has also the advantage of allowing easily the generalization of geometry to Euclidean spaces of more than three dimensions.
（2）Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics, including in general relativity.