Cartesian coordinate system
The term Cartesian originates from the last name of the famous French philosopher, René Descartes (Rene Descartes) in tribute to his profound system of investigation published anonymously in 1637 titled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences. It is commonly referred to as Discourse on Method. In part two, he introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as measuring guides; he further explores this in Geometry, book two of the volume as it was originally published. This idea provided the bridge between ancient Greek Euclidean geometry and algebra, leading to a revolution in math and science. It is one of the important tools used in analytic geometry, calculus, and cartography.
The modern Cartesian Coordinate System is commonly defined by two axes, at right angles to each other, forming a plane (an xy-plane). The horizontal axis is labeledx, and the vertical axis is labeled y. In a three dimensional coordinate system, another axis, normally labeled z, is drawn orthogonally, providing a sense of a third dimension of space measurement. (Early systems allowed "oblique" axes, that is, axes that did not meet at right angles.)
The point of intersection, where the axes meet, is called the origin. To specify a particular point on a two dimensional coordinate system, you indicate the x unit first, followed by the y unit in the form (x,y). In three dimensions, a third z unit is added, (x,y,z).
The choices of letters come from the original convention, to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values.
Example of two dimensional cartesian coordinate system:
http://www.wikipedia.com/images/uploads/cartesiancoordinates2D.JPG
The intersection of the two x-y 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). Normally quadrant I contains all real numbers greater than 0 for both x and y measurements, quadrant II contains all numbers less than 0 for x and all 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.)
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 a three-dimensional coordinate system...
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 specialized ends.
It may be interesting to note that some have indicated that the master artists of the Renaissance used a grid, 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.
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