Coordinate System

A reference frame is a standard point of view or a perspective chosen to display quantitative measurements about places of interest in a space and the phenomena that take place there.

To be suited for this quantitative purpose, a reference frame needs to include a coordinate system. This is a system of assigning locations to points of space and time. In physics it is generally assumed that space is a three-dimensional Euclidean manifold, where each spatial point is to be assigned three real numbers for its location in space. These numbers are called coordinates.

Any point $P$ in Euclidean space may be represented by the ordered triple of real numbers $(x, y, z)$ called the Cartesian coordinates of $P$ .

These coordinate numbers are the values of the perpendicular projections of the point $P$ onto three arbitrary, but mutually orthogonal, coordinate axes from a chosen origin point $O$ .

There are many possible reference frames. To choose a reference frame is to select an origin and the coordinate axes that orient the frame in space.
The Cartesian coordinate system is preferred by physicists because its coordinate axes are mutually perpendicular; all Euclidean spaces can have Cartesian coordinate systems.