RENE DESCARTES

Mathematician and Father of Modern

Philosophy and the Coordinate

Plane

1595-1650

Rene Descartes was born in 1595 in LaHaye, France. His village has now been renamed Descartes, France in his honor. His father was a wealthy lawyer, judge and member of the French parliament. His mother died shortly after Rene was born.

Rene was a frail, sickly child, but was extremely intelligent. He left for college in 1606 (when he was just 11 years old).

In college, Rene studied many subjects but he loved math the most. He is quoted as saying, “With me, everything turns into mathematics.”

Since Rene was so sickly, he was given special privileges by the college he attended. The other students had to get up at 5:00 a.m. for classes, but Rene was allowed to sleep until 10:00 a.m.

After graduating, Rene attended law school (at the request of his father) and received a degree in law at the age of 20. He also earned degrees in Mathematics, Philosophy and the Sciences.

At the age of 23, Rene moved to the Netherlands to work with some very famous mathematicians there. He also had grown to love philosophy so he continued to study that as well.

At this time, he also began writing many books.

One of the very important areas of math that was being studied during Descartes’ life was Geometry. Shapes, especially circles and their properties were very important to mathematicians of the time.

Rene and another mathematician named Fermat worked together to find a way to describe curves and shapes in Geometry using Algebra.

Descartes and Fermat came up with a system we now call coordinate geometry in which we can take algebraic equations and plot them to show what they look like. This is done on the Coordinate Plane using coordinates which are also called ordered pairs.

We will take a look at this system in a minute.

When Rene was 54 years old, he was one of the most well known mathematicians of his time. The Queen of Sweden hired him as her personal mathematician.

Unfortunately, she required him to get up early and walk in the cold weather of Sweden to the castle to work for her.

Within less than a year, he fell ill and died at the age of 55.

THE COORDINATE PLANEOR CARTESIAN COORDINATE SYSTEM

This is the system Descartes and Fermat invented.

x

y

The Coordinate Plane is made up of 2 axes, the x-axis and the y-axis.

The x-axis is horizontal and the y-axis is vertical.

The 2 axes cross at a point called the ORIGIN.

The four sections of a coordinate plane are called the quadrants. They are labeled with Roman numerals going counterclockwise.

III

III IV

Coordinates – ordered pairs of numbers that give the location a point on a grid.

Here are some examples of coordinates: (1, 2) (3, -4) (-5, 0)

The first number is always the x. It tells you how far to go left or right on the x axis.

The second number is always the y. It tells how far to go up or down on the y axis.

RIGHT AND UP ARE POSITIVE DIRECTIONS

LEFT AND DOWN ARE NEGATIVE

DIRECTIONS

Let’s take a look at how to plot some points.

(3,2) The x value is 3 and the y value is 2. Since they are both positive numbers, we will go right 3 and up 2.

(3,2)

The coordinate ( -2, 1) would go left 2 and up 1.

The coordinate ( 3, -2) would go right 3 and down 2.

Which directions would you use for the coordinate (-4, -2)?

Let’s take a look at the coordinate plane poster on the front board to identify and plot some more coordinates.