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Return to book index Chapter 1 : Connections to Algebra

René Descartes

Born in France in 1596, René Descartes, mathematician, scientist, and philosopher, is among the most acclaimed scholars in history.

Descartes and Philosophy

Descartes has sometimes been referred to as the father of modern philosophy, and is perhaps best known for expressing the axiom "Cogito, ergo sum," or "I think, therefore I am." In 1637, he published his most famous philosophical work, Discours de la Méthode (Discourse on Method). In this work, he describes some rules for the pursuit of knowledge:

  • accept something as true only if you believe it to be so
  • solve problems systematically by analyzing them piece by piece
  • consider the simple things first, then the more complex ones
  • review your work to make sure you haven't left anything out

Descartes and Mathematics

Descartes published La Géométrie in 1637, as part of Discours de la Méthode. In La Géométrie, Descartes first showed how to use a coordinate system to visually represent algebraic equations. In doing so, he closely linked geometry and algebra, and paved the way for future innovations in two- and three-dimensional visual representations.

The coordinate system is the basis of all visual representations that are computer-drawn and represented as pixels. Pixels are the smallest image-forming unit of a video display. For example, if a computer's video display has a resolution of 1024 by 768, this is another way of saying that it represents images on the video display using a type of coordinate plane that measures 1024 units by 768 units.

The coordinate system has also been adapted to three dimensions for use in important innovations. Some of these include CT scanning, a medically useful method of taking three-dimensional pictures of internal organs, and the Global Positioning System (GPS), which uses satellites and computers to pinpoint the location of an object on Earth.