In mathematics, coordinate system is a method to describe and locate the position of points in a plane or space. A coordinate system consists of a coordinate axis and an origin, wherein the coordinate axis is a straight line arranged by numerical values, and the origin is the intersection point of the coordinate axis. In two-dimensional coordinate system, we usually use X axis and Y axis to describe the position of points, and in three-dimensional coordinate system, we need to add Z axis. The establishment of coordinate system can make us better understand and express various mathematical and scientific problems, such as geometry, algebra, physics and so on.

There are many kinds of coordinate systems, the most common one is Cartesian coordinate system, also called Cartesian coordinate system, which consists of two vertical coordinate axes. This coordinate system is often used in geometry, algebra and physics. There are polar coordinate system, spherical coordinate system and so on. Polar coordinate system describes the position of a point by its distance from the origin and its included angle with the positive semi-axis of X axis, while spherical coordinate system describes the position of a point by its distance from the origin, its included angle with the positive semi-axis of Z axis and its projected included angle with the positive semi-axis of X axis. Different coordinate systems are suitable for different problems and need to be used flexibly.

Coordinate system has a wide range of applications, including mathematics, physics, engineering, computer science and so on. In computer science, coordinate system is often used to describe the position of graphics and controls in the graphical interface. In spatial planning and urban planning, the coordinate system can be used to determine the coordinates of buildings and the location of the city center. In the field of navigation, coordinate system can be used to determine the position of a car or an airplane in space and calculate the shortest path and the fastest speed. It can be said that the coordinate system is one of the indispensable foundations of modern science and technology.