Cartesian Coordinates: A system used for locating objects on a surface or in space.

A Cartesian coordinate system with two dimensions consists of two infinitely long number lines, also called "axes", one of which is placed over the other. Accordingly, three dimensions require three number lines. Each point of the surface or space is indicated by by two or three positions on the number lines, thus by two or three numbers. The below example illustrates a two-dimensional coordinate system with a position indicated by the numbers 2 and 4 in the space in which the dotted lines touch:

The Cartesian coordinate system was invented by René Descartes and has been used in mathematics ever since to represent geometric objects or curves. At the end of the 19th century Georg Cantor proved that any given surface or space contains just as many points as a line (for the proof, see the article on dimension). Prior to that, Bernard Bolzano showed that the number of points on a line does not depend on its length. Accordingly, any given section of any Cartesian coordinate system, regardless of its dimensionality, contains exactly as many points as any other.

© Johann Christian Lotter   ■  Infinity  ■  Links  ■  Forum