Descartes and the Cartesian Plane

10 Apr

The Cartesian Plane, also known as the Coordinate Plane, is named after the French mathematician René Descartes. He was born in La Haye, France on March 31, 1596. Descartes was taught at home up to the age of eight. At that point, he entered the Jesuit college of La Flèche, where he continued his schooling until graduating at the age of eighteen.

While at La Flèche, Descartes suffered health problems and because of this, his teachers allowed Descartes to stay in bed for most of the morning. Even though he missed almost all of his morning classes, he was still able to keep up with all of his studies. It has been rumored that Descartes’ inspiration for the coordinate plane came about because of all the time he spent in bed. The story goes that one day when Descartes was in bed, he noticed a fly crawling around on the ceiling. He tried to think of ways to describe where the fly was located and realized that he could do so by describing the fly’s position by its distance from each wall. Then he tried to relate the fly’s position to a point, and, well, one thing lead to another, and voilà! He came up with the coordinate plane and Cartesian coordinates!

Cartesian coordinates are used to locate a point in space by giving its relative distance from perpendicular intersecting lines. These perpendicular intersecting lines for the two coordinate axes of the Cartesian (coordinate) plane. Any point, line, or figure can be precisely located by referencing these axes. The horizontal axis is called the x-axis, and the vertical axis is called the y-axis. The coordinate plane is divided into four quadrants (as pictured below).

In the system that Descartes created, a coordinate pair (or an ordered pair) is what describes the location of a point in the coordinate plane. The coordinate pair, in general, is (x, y). The first value is the x-coordinate, which describes where on the x-axis the point is located. The second value is the y-coordinate, which describes where on the y-axis the point is located. By using the Cartesian coordinate system, any point in the plane can be described using a pair of coordinates.

The location of a city, country, or a ship at sea is given by a set of coordinates, and another application of ordered pairs is that computer graphic artists create figures and computer animations by referring to coordinates. What else are ordered pairs used for in the real world? Post responses below! 🙂

Source (MLA Format): “Descartes and His Coordinate System.” Book Rags. Web. 09 Apr. 2012. <http://www.bookrags.com/research/descartes-and-his-coordinate-system-mmat-02/&gt;.

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One Response to “Descartes and the Cartesian Plane”

  1. charlieszr4 April 10, 2012 at 8:41 am #

    Architects use ordered pairs, they use them to show the length of sides of objects like walls, roofs, etc. in blueprints.

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