1. Analysis of functions and construct graphs
Miguel Barão
Number: 15
11th Form
Class A

2. Table of Contents Introduction René Descartes: Biography
History of the Cartesian coordinate system
Cartesian coordinate system
Conclusion
Bibliography

3. The four quadrants of a Cartesian
Introduction
In order to participate in this project, I made this presentation about the subtopic “Analysis of functions and construct graphs”, and I have chosen the mathematician René Descartes, and his theory: “Cartesian coordinate system”.
I think this topic is very interesting because every day we see this theory applied statistical graphs, for example, about economical stats.
René Descartes
Cartesian Graph
The four quadrants of a Cartesian

4. René Descartes
Rene Descartes was a famous French mathematician, scientist and philosopher. He was the first major philosopher in the modern era to make a serious effort to defeat skepticism.
Descartes was born at La Haye and educated at the Jesuit College of La Flèche between 1606 and  
One of the most notable theories of Rene Descartes was the Cartesian Geometry, which uses algebra to describe geometry. He "invented the convention of representing unknowns in equations by x, y.

5. History of the Cartesian coordinate system
The idea of the Cartesian Coordinate System was developed in 1637 by Descarts and independently by Pierre de Fermat, the last one used three dimensions, but Pierre never published his discovery. René Descartes introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as guides. This discovery allowed the development of perspective and projective geometry. Before the time of Descarts, Nicole Oresme, a French philosopher of the 14th Century, used constructions similar to the cartesian coordinates.
Many others coordinate systems have been also developed, such as the cylindrical coordinates for three-dimensional space.
René Descartes
Pierre de Fermat

6. Cartesian coordinate system
A coordinate system is a system that uses one or more numbers, or coordinates, to determine the position of a point or geometric element. In elementary mathematics the coordinates of this system are real numbers, but in complex system can complex numbers.
Coordinates: The numbers in a ordered pair which locate a point in the coordinate plane.
Ordered pair: A pair of numbers (x,y), that represents a point on a coordinate grid.

7. Cartesian coordinate system
X-axis: The horizontal number line on a coordinate graph.
Y-axis: The vertical number line on a coordinate graph.
Quadrants: The four parts made by X and Y axis. (I, II, III, IV)
Origin: Intersection of X and Y axis. (0,0)
Coordinates: Always write the “x” value first and then the “y” value, for example: (x,y) on plan or (x,y,z) on space.
y-axis
Number line
Origin
x-axis
Cartesian Graph (Plan)
Quadrants of a Cartesian Graph

8. Conclusion
Summing up, every day, in our lives, we use the Cartesian Coordinate System, and this system is much useful. With this discovery of René Descartes, is now much simply to create and understand graphs in the plan or in the space.
I found this work very interesting and this has allowed me to widen my knowledge about the history of mathematic.

9. Bibliography Images from Google Images.