Editing Cartesian coordinate system (section)

==History==
{{Descartes}}
The adjective ''Cartesian'' refers to the French [[mathematician]] and [[philosopher]] [[René Descartes]], who published this idea in 1637 while he was resident in the Netherlands. It was independently discovered by [[Pierre de Fermat]], who also worked in three dimensions, although Fermat did not publish the discovery.<ref>{{Cite web|url=https://www.britannica.com/topic/analytic-geometry|title=Analytic geometry|last1=Bix|first1=Robert A.|last2=D'Souza|first2=Harry J.|website=Encyclopædia Britannica|access-date=2017-08-06}}</ref> The French cleric [[Nicole Oresme#Mathematics|Nicole Oresme]] used constructions similar to Cartesian coordinates well before the time of Descartes and Fermat.<ref>{{harvnb|Kent|Vujakovic|2017|loc=See [https://books.google.com/books?id=EVRSDwAAQBAJ&q=Nicole+Oresme+coordinate&pg=PT307 here]}}</ref>

Both Descartes and Fermat used a single axis in their treatments and have a variable length measured in reference to this axis.<ref>{{Cite book |last=Katz |first=Victor J. |url=https://www.worldcat.org/title/71006826 |title=A history of mathematics: an introduction |date=2009 |publisher=Addison-Wesley |isbn=978-0-321-38700-4 |edition=3rd |location=Boston |pages=484 |oclc=71006826}}</ref> 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. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes's work.<ref>{{harvnb|Burton|2011|loc=p. 374}}.</ref>

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]].<ref>{{harvnb|Berlinski|2011}}</ref> The two-coordinate description of the plane was later generalized into the concept of [[vector spaces]].<ref>{{harvnb|Axler|2015|p=1}}</ref>

Many other coordinate systems have been developed since Descartes, such as the [[Polar coordinate system|polar coordinates]] for the plane, and the [[Spherical coordinate system|spherical]] and [[Cylindrical coordinate system|cylindrical coordinates]] for three-dimensional space.