1. Co-ordinate (or Cartesian) Geometry
René Descartes
Co-ordinate (or Cartesian) Geometry

2. René Descartes (1596 – 1650)
René Descartes was a French philosopher whose work, La géométrie, includes his application of algebra to geometry from which we now have Cartesian Geometry. His work had a great influence on both mathematicians and philosophers.

3. Quotations by René Descartes
Cogito Ergo Sum. "I think, therefore I am." Discours de la Méthode
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery. La Géométrie.
Omnia apud me mathematica fiunt. With me everything turns into mathematics.

4. Descartes was educated at the Jesuit college of La Flèche in Anjou
Descartes was educated at the Jesuit college of La Flèche in Anjou. He entered the college at the age of eight years, in He studied there until 1612, studying classics, logic and traditional Aristotelian philosophy. He also learnt mathematics from the books of Clavius. While in the school his health was poor and he was granted permission to remain in bed until 11 o'clock in the morning, a custom he maintained until the year of his death.
School had made Descartes understand how little he knew, the only subject which was satisfactory in his eyes was mathematics. This idea became the foundation for his way of thinking, and was to form the basis for all his works.
In 1649 Queen Christina of Sweden persuaded Descartes to go to Stockholm. However the Queen wanted to draw tangents at 5 a.m. and Descartes broke the habit of his lifetime of getting up at 11 o'clock. After only a few months in the cold northern climate, walking to the palace for 5 o'clock every morning, he died of pneumonia.

5. Legend has it that, while lying in bed one morning, René observed a fly walking across the tiled ceiling above him and came up with the idea of the cartesian co-ordinate system to describe the position of the fly on the ceiling.

6. Two-dimensional coordinate system
The four quadrants of a Cartesian coordinate system. The arrows on the axes indicate that they extend forever in their respective directions (i.e. infinitely).

7. In mathematics, the Cartesian co-ordinate system (also called rectangular co-ordinate system) is used to determine each point uniquely in a plane through two numbers, usually called the x-co-ordinate and the y-co-ordinate of the point. To define the co-ordinates, two perpendicular directed lines (the x-axis, and the y-axis), are specified, as well as the unit length, which is marked off on the two axes.

8. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by algebraic equations, namely equations satisfied by the coordinates of the points lying on the shape. For example, the circle of radius 2 may be described by the equation x2 + y2 = 4.

9. Three-dimensional coordinate system
Three dimensional Cartesian co-ordinate system with y-axis pointing away from the observer.

10. The three dimensional Cartesian co-ordinate system provides the three physical dimensions of space — length, width, and height.
Three dimensional Cartesian co-ordinate system with the x-axis pointing towards the observer.

11. It may be interesting to note that some have indicated that the master artists of the Renaissance used a grid, in the form of a wire mesh, as a tool for breaking up the component parts of their subjects they painted. That this may have influenced Descartes is merely speculative.
Albrecht Dürer's interpretation of ‘The Draftsman’s Net’.

12. René Descartes with Queen Christina of Sweden.
One of Descartes most enduring legacies was his development of Cartesian geometry which uses algebra to describe geometry. He also invented the notation which uses superscripts to indicate powers or exponents, for example the 2 used in x² to indicate squaring.
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