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 Did you know . . .?


The man who invented analytic geometry, René Descartes (1596-1650), never got out of bed before 11 in the morning!

Illustration of Cartesian coordinate systemAnalytic geometry brings together the analytical tools of algebra and the visual immediacy of geometry by providing a way to visualize algebraic functions. Descartes, a French philosopher and mathematician, did this through the introduction of the coordinate system that still bears his name, the Cartesian coordinate system. Descartes published his ideas in 1637 in a treatise called La géométrie (Geometry).

It is said (although the story is probably a myth) that Descartes came up with the idea for his coordinate system while lying in bed and watching a fly crawl on the ceiling of his room.

Portrait of Descartes







René Descartes.

(Source: http://www.ga.k12.pa.us/academics/US/Math/Millar/Descartes/Burka.htm)

Descartes' Geometry was an appendix to a larger work called Discourse on the Method of Properly Conducting One's Reason and of Seeking the Truth in the Sciences. In this work, Descartes set out to place human knowledge on a new, firm footing, an important task in an age beset with doubts and controversy and in which skepticism reigned. Descartes himself had seen service in warfare spurred by religious disagreements, and he was no stranger to scientific controversy, either. In 1633, hearing that Galileo had been condemned for teaching that the earth moved around the sun, Descartes abruptly decided not to publish a work defending the idea of a sun-centered univierse.

Descartes found a model for proper reasoning in mathematics, especially in geometry, and his appendix on Geometry was meant to illustrate the effectiveness and usefulness of his method. His method was based on four basic rules for deducing knowledge in the manner of a geometry proof. His famous line, "I think, therefore I am," reveals the first firm piece of knowledge upon which his subsequent deductions were based.

In 1649, Descartes accepted an invitation from Queen Christine of Sweden to move to the Swedish court in Stokhlom and become her private tutor. His new employer, however, forced him to begin lessons at 5 a.m.! For a man who had stayed in bed till 11 since childhood, this early rising, combined with the cold climate, proved to be too much. He died of a lung inflammation on February 11, 1650.


In his own words:

I thought the following four [rules] would be enough, provided that I made a firm and constant resolution not to fail even once in the observance of them. The first was never to accept anything as true if I had not evident knowledge of its being so; that is, carefully to avoid precipitancy and prejudice, and to embrace in my judgment only what presented itself to my mind so clearly and distinctly that I had no occasion to doubt it. The second, to divide each problem I examined into as many parts as was feasible, and as was requisite for its better solution. The third, to direct my thoughts in an orderly way; beginning with the simplest objects, those most apt to be known, and ascending little by little, in steps as it were, to the knowledge of the most complex; and establishing an order in thought even when the objects had no natural priority one to another. And the last, to make throughout such complete enumerations and such general surveys that I might be sure of leaving nothing out. These long chains of perfectly simple and easy reasonings by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or to well hidden to be discovered.
Discours de la Méthode. 1637.

Omnia apud me mathematica fiunt.
With me everything turns into mathematics.

Cogito ergo sum. "I think, therefore I am."
Discours de la Méthode. 1637.

It is not enough to have a good mind. The main thing is to use it well.
Discours de la Méthode. 1637.

If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.
Discours de la Méthode. 1637.

(Source: http://www-groups.dcs.st-andrews.ac.uk/~history/Quotations/Descartes.html)


Fun links:

Page with dynamic applets for graphing on the Cartesian and other coordinate systems: http://www.univie.ac.at/future.media/moe/galerie/zeich/zeich.html

Application to convert between Cartesian and polar coordinates: http://qmc.yi.org/mrtutor/math/CoordScript.html

Graph sketcher application for sketching functions on the Cartesian coordinate system (Be sure to click the "How?" button for insturctions on how to type in mathematical symbols!): http://www.shodor.org/interactivate/activities/sketcher/index.html

Maze game using the Cartesian coordinate system: http://www.shodor.org/interactivate/activities/coords/index.html

For more information:







By Laura Smoller, UALR Department of History.

March 2001.