Cartesian coordinate system
The name Cartesian is in direct attribution to its originator, René Descartes (Rene Descartes) who introduced the new idea of specifying the position of a point on a surface with the use of two intersecting lines as measuring guides. This method of specifying position on a plane has been used in cartography and has been observed as the bridge between ancient Greek Euclidean geometry and algebra.
The Cartesian Coordinate System is commonly defined by two axes, at right angles to each other, labeled y on the vertical axis and labeled x on the horizontal axis by convention. When working in a third dimension of measurement, another axis labeled z is drawn orthogonally to give the sense of a third dimension of space measurement. The intersection of the axes is called the origin, whose coordinate is indicated by the symbolization: (0,0). In order to name or specify a point on a plane created by the intersection of two axes, we can take a measurement from each axis and indicate the value in the form, (x,y) or, in three dimensions, (x,y,z).
The intersection of the two axes creates four quadrants indicated by the roman numerals I, II, III, and IV. By normal convention, the quadrants are labeled counter-clockwise starting from the northeast quadrant. An example of a point P on the system is indicated below by P(5,2). It is common, when the quadrants are labeled in this fashion, that quadrant I contains all real numbers greater than 0 for both x and y measurements, quadrant II contains all negative numbers less than 0 for x and all positive numbers greater than 0 for y. (III contains only negative points for both axes, and IV contains positive numbers for x and negative for y, see table below.)
/\\
|
| y
|
II | I
|
| .P(5,2)
|
<--------------------------------> x
|
|
III | IV
|
|
|
\/
Quadrant |
x values |
y values |
I |
>0 |
>0 |
II |
<0 |
>0 |
III |
<0 |
<0 |
IV |
>0 |
<0 |
The arrows on the axes indicate that they extend forever in the same direction (i.e. infinitely).
In analytic geometry the Cartesian Coordinate System is the foundation for the algebraic manipulation of geometrical shapes. Many other coordinate systems have been developed since Descartes. One common system uses polar coordinates. In different branches of mathematics coordinate systems can be transformed, translated, and re-defined altogether to simplify calculation and for other specialized purposes.
It may be interesting to note that some have indicated that the master artists of the Renaissance used a grid to look through, in the form of a wire mesh, as a tool for breaking up the component parts of their subjects they painted--a trade secret. That this may have influenced Descartes is merely speculative.