( ) Mathematician ÖZGÜR MUSTAFA SUCU CMPE220 FALL 2008

Background Information Born March 31, 1596 in France Mother died of Tuberculosis when he was 1 year old Father was a judge in the High Court of Justice At age 10 attended the Jesuit College Royal Henry-Le-Grand Delicate health issues-permitted to lie in bed till late in the mornings Graduated and went to the University of Poitiers with a law degree in 1616, but never practiced law

Background Continued… In the army for a couple years Traveled for 5 years Devoted the rest of his life to philosophy and mathematics Published a lot of his works

Contributions Systematization of analytic geometry First to attempt to classify curves according to the types of equations that produce them Theory of equations Law of Conservation of Momentum Last letters of the alphabet are unknown quantities and first letters are known ones Rule of Signs Exponential notation Cartesian geometry

MORE DETAILED... As the inventor of the Cartesian coordinate system, Decartes founded analytic geometry, the bridge between algebra and geometry, crucial to the invention of calculus and analysis. Descartes' reflections on mind and mechanism began the strain of Western thought that much later, impelled by invention of the electronic computer and by the possibility of machine intelligence, blossomed into the Turing test and related thought.

Descartes' theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. Descartes' rule of signs is also a commonly used method to determine the number of positive and negative zeros of a polynomial. He invented the notation which uses superscripts to show the powers or exponents, for example the 2 used in x 2 to indicate squaring.

Cartesian geometry  vector space  definition of the plane  distance problems  the dot product, to get the angle of two vectors  the cross product, to get a perpendicular vector of two known vectors (and also their spatial volume)  intersection problems

The Cartesian Coordinate System Descartes developed the coordinate plane system which is widely used today

Tangents to Curves Descartes did a lot of work about tangents to curves. He illustrated his theory by giving the general rule for drawing tangents and normals with a circle.

In Closing… Died at Stockholm, Sweden on February 11, 1650 of pneumonia “Founder of Modern Philosophy” “Father of Modern Mathematics” French philosopher, scientist, and mathematician Most famous for finding analytical geometry Cogito ergo sum (I think, therefore I am)

REFERENCES    student.valpo.edu/kgross/portfolio/Rene%20Descartes. ppt

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