Cartesian coordinates, also called rectangular coordinates, provide a method of rendering graphs and indicating the positions of points on a two-dimensional (2D) surface or in three-dimensional ( 3D ) space. The scheme gets its name from one of the first people known to have used it, the French mathematician and philosopher René Descartes (1596-1650). The Cartesian coordinate system is used to define positions on computer displays and in virtual reality (VR) renderings. The system is also employed in mathematics, physics, engineering, navigation, robotics , economics, and other sciences.
The Cartesian plane consists of two perpendicular axes that cross at a central point called the origin. Positions or coordinates are determined according to the east/west and north/south displacements from the origin. The east/west axis is often called the x axis, and the north/south axis is called the y axis. For this reason, the Cartesian plane is also known as the xy -plane. The x and y axes are linear number lines, meaning that each division on a given axis always represents the same increment. However, the increments on different axes can differ. For example, in the illustration at left below, each increment on the x axis might represent 2 units, while each increment on the y axis represents 5 units. Points or coordinates are indicated by writing an opening parenthesis, the x value, a comma, the y value, and a closing parenthesis in that order. An example is ( x,y ) = (2,-5). The origin is usually, but not always, assigned the value (0,0).
Cartesian three-space, also called xyz -space, has a third axis, oriented at right angles to the xy -plane. This axis, usually called the z axis, passes through the origin of the xy -plane. Positions or coordinates are determined according to the east/west ( x ), north/south ( y ), and up/down ( z ) displacements from the origin. As is the case with the x and y axes, the z axis is a linear number line. For example, in the illustration at right above, each increment on the x axis might represent 5 units, each increment on the y axis 10 units, and each increment on the z axis 2 units. Points or coordinates are indicated by writing an opening parenthesis, the x value, a comma, the y value, another comma, the z value, and a closing parenthesis in that order. An example is ( x,y,z ) = (5,-10,-4). The origin is usually, but not always, assigned the value (0,0,0).
22 Mar 2011