Analysis of functions and construct graphs

Miguel BarãoNumber: 1511th FormClass A

Table of Contents

Introduction René Descartes: Biography History of the Cartesian coordinate system Cartesian coordinate system Conclusion Bibliography

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

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 1614.

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.

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

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.

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

Origin

x-axis

Number line

Quadrants of a Cartesian GraphCartesian Graph (Plan)

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.

Bibliography

Images from Google Images.

http://en.wikipedia.org/wiki/Coordinate_system

http://www.authorstream.com/Presentation/aSGuest11646-143630-coordinate-syst

em-created-girish-graphs-education-ppt-powerpoint/