René Descartes
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René Descartes was born in « La Haye », near Tours (now named Descartes), on
March 31st 1596 and died in Stockholm on February 11th 1650.
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He was a mathematician, a physicist, and a philosopher.
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His father was a Member of Parliament and his mother died when he was only one.
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This brilliant mathematician was raised by his grand-mother.
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He studied ancient literature and Aristotle’s philosophy with the Jesuits.
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He obtained a degree in law and enrolled in the army at the beginning of the so-called
‘30-year war’ (1618 – 1638). But he quit soon and started to learn sciences and
travelled all around Europe to meet famous scholars. He gave advice to Blaise Pascal,
another famous mathematician and philosopher of his time.
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In 1628, he started studying philosophy in Holland where he wrote “Philosophical and
Mathematical Reflections”, which was heavily criticized. However, he’s now
considered as one of the founders of modern philosophy, according to Hegel.
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He was convinced that there was “unity in knowledge”, so he created the “sensible
reasoning of thought”. He wrote the now famous sentence: “I think, therefore I am”.
He even tried to prove the existence of God, and said that all truth came from Him.
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In mathematics he created the Cartesian coordinate system which was later adopted by
many scientists such as Galileo and Kepler.
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In physics, he discovered the refraction laws in optics, and his assumptions on the
solar system were proved to be true.
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Einstein said he was in advance of his time in comparison with Newton.
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In philosophy, he insisted on the notion of free will, redefining morality and ethics.
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In conclusion, he was much more than just a mathematician. He was interested in
many and various subjects. He is remembered by his scientific research, his numerous
proofs in mathematics, and his philosophy with the essay on the existence of God.
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Here is a list of his most famous books:
In philosophy:
- « Le Discours de la Méthode », 1637
- « Méditations Métaphysiques », 1641
- « Les principes de la philosophie », 1644
- « Règles pour la Direction de l’Esprit » published in 1701, after his death.
In sciences:
- « La géométrie », 1637
- « La dioptrique », 1673
Descartes’ geometry
In geometry, Descartes’ theorem,
establishes a relationship between four
tangent circles. It can be used to draw
the circle which is tangent to three
circles already tangent to each other.
He defined what a curvature is. The
curvature of a circle is defined by
where is the circle’s radius.
The larger the circle, the smaller the
curvature, and vice versa.
The “+”sign is used for a circle which is tangent “externally to other circles (as the three black
ones). If the circle is tangent internally (as the big red one), the sign “–” is used.
Cartesian coordinates:
Coordinates are used to describe the position of points, straight lines, surfaces or portions of
space.
The most famous system is Descartes’ one: the Cartesian coordinates, based on perpendicular
axes. This French scientist invented a system to define the position of any point in a plane
using a pair of numbers.
Firstly, a system of two perpendicular straight lines is built. Each line is called a coordinate
axis of the system, and the point where they meet is the origin, which is given the coordinates
(0, 0).
For the horizontal axis we count positively to the right of the origin and negatively to the left.
For the vertical axis we count positively above the origin and negatively below. On the
horizontal axis numbers are called “x”. On the vertical one numbers
are called “y”.
For example, if we want to know the coordinates of a point P, we
draw from that point two lines perpendicular to the x- and y-axis.
Their intersections with each axis tell us the value of “x” and of “y”.
This defines the position of the point.
It is extraordinary that this system works in 2 dimensions but
also in 3 dimensions. In this case, we have to add a third
coordinate: “z”. For example, imagine a point P above a piece of
paper. If we want its coordinates in space we already have the xand y-coordinates of the point which is directly below it on the
paper. We measure the distance above the paper by the number
z to give P its three coordinates :(x,y,z).
You will probably notice that with Cartesian coordinate, we’re
using many conventions.
-The first one is to write the Cartesian coordinates of a point by using brackets and separating
the numbers with commas, as in (10, 5).
-Then, the origin is often noted with the capital letter O.
-In analytical geometry, unknown or generic coordinates are usually written by using the
letters x and y for the plane, and x, y, and z for three-dimensional space.
This custom comes from an old convention of algebra, to use letters near the end of the
alphabet for unknown values.
-Another common convention for naming coordinates is to use subscripts, such as x1, x2, ... xn
for n coordinates.
QUESTIONS TEST:
- Pascal, Newton, Descartes
- Aristotle, Descartes, Einstein, Descartes