The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space.ĭescription One dimension įurther information: Two-dimensional spaceĪ Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system ) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis.
The two-coordinate description of the plane was later generalized into the concept of vector spaces.
The development of the Cartesian coordinate system would play a fundamental role in the development of the calculus by Isaac Newton and Gottfried Wilhelm Leibniz. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes' work. The concept of using a pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649 by Frans van Schooten and his students. īoth Descartes and Fermat used a single axis in their treatments and have a variable length measured in reference to this axis.
The French cleric Nicole Oresme used constructions similar to Cartesian coordinates well before the time of Descartes and Fermat. It was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. The adjective Cartesian refers to the French mathematician and philosopher René Descartes, who published this idea in 1637.