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Rene Descarte - Mathematician

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Published in: Mathematics
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All about the Mathematician - Rene Descarte

Sumayya H / Dubai

2 years of teaching experience

Qualification: B.Ed (pursuing : 2020 - 2022), MSc Mathematics

Teaches: Maths, Mathematics

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  1. RENÉ DESCARTES (1596 - 1650)
  2. René Descartes (March 31, 1596 - February 11, 1650) was a highly influential French mathematician, philosopher, scientist and writer was born near Tours. He is also known as Renatus Cartesius. He has been dubbed the "Father of Modern Philosophy" Descartes is often regarded as the first modern thinker to provide a philosophical framework for the natural sciences as these began to develop.
  3. When he was one year old, his mother Jeanne Brochard died of tuberculosis. His father Joachim was a judge in the High Court of Justice.
  4. At the age of eight, he entered the Jesuit College Royal Henryé-Le-Grandat La Fleche. After graduation, he studied at the University of Poitiers, earning a Baccalaureate and License in law in 1616, in accordance with his father's wishes that he should become a lawyer but he never practiced law. In succeeding years Descartes served in other armies, but his attention had already been attracted to the problems of mathematics and philosophy to which he was to devote the rest of his life.
  5. His accidental encounter with Isaac Beeckman, the head of the Dutch College at Dort, aroused his mathematical interest and found a solution for a geometrical problem which was a challenge to the entire world. Impressed by the certainity of mathematical proofs and evidence of reasoning — mathematics favourite subject Used math in Military engineering, meteorological observations, studies on glaciers and heights of mountains.
  6. In 1628, Descartes moved to Holland and lived there for twenty years giving up all his time to philosophy and mathematics. He received traditional education in Mathematics, Physics, Logic and Ancient languages. Descartes was also one of the key figures in the Scientific Revolution.
  7. Discourse (1637) on the method of properly Guiding the Reason in the Search for Truth in the Sciences. FAMOUS WORKS DISCOURSE ON METHOD REN DESCARTES The Meditations on First Philosophy (Demonstrating the existence of God and the distinction between mind and body).
  8. La Géométrie (1 637), on analytic geometry and included an analysis of the algebra then current. GEOMETRIE In the year 1 644, he brought out his another work Principles of Philosophy. In 1649, after completing his another work 'Passions of the Soul' he was invited by Queen Christina to come to Sweden for providing instructions to her.
  9. The queen fixed 5'0 clock in the morning for her tuition. The great mathematician could not tolerate the severeness of the climate and as a result of exposure of the severe chill in the bitter morning died on February 11, 1 650 having passed about four months in Sweden.
  10. FAMOUS STATEMENT His most famous statement is: Cogito ergo sum (French: Je pense, donc je suis; English: I think, therefore I am; OR I am thinking, therefore I exist), found in part I of Principles of Philosophy (Latin) and in part IV of Discourse on the Method (French).
  11. CONTRIBUTIONS Descartes' influence in mathematics is also apparent, the Cartesian coordinate system which uses algebra to describe geometry. This also paved the way to the invention of differential calculus and analysis which made Newton and Leibnitz immortal mathematicians. Quadrant Quadrant m y axis upward and to the t Quadra nt IV
  12. His work changed the face of Mathematics because he founded Analytical Geometry. Parabola Circle Ellipse Analytical Geometry Hyperbola
  13. It was Descartes who first set the practice of denoting variables by x, y, z and constants by a, Descartes devised a method of determining the shortest line PQ from a given point P to a given curve (this line is now called normal). He also introduced the rule for finding the limit to the number of positive and negative roots of an algebraic equation, and the method of indeterminate coefficients for the solution of equations.
  14. He also invented the notation which uses superscripts to show the powers of exponents. A-le solved the problems of doubling a cube and trisecting an angle. He enunciated the theorem on the relation between the number of faces, edges and angles of a polyhedron. > Descartes distinguished between two classes of curves : geometrical and mechanical, or as Leibnitz preferred to call them : algebraical and transcendental.
  15. Most significant contribution lies in the integration and harmonization of different branches of knowledge. His attempts to introduce the rigor and clarity of math into philosophy and sciences. find unity in different mathematical branches. reconstruct and interrelate non-mathematical sciences with reasoning.
  16. He also discovered an interesting curve, called Cartesian Oval that led to far-reaching research in geometrical analysis.
  17. advocated three kinds of operations in mathematical reasoning intuitus : non-inferential act of direct prehension, error free, we conceive just a single term simple or complex (Straightness, sphere). deductio : not deduction but elicits a series of successively intuited terms with relations between them. Analytic and synthetic procedure i.e., simple to complex and vice versa. enumeratio : is to avoid error due to faulty memory in case of numerous deductive steps to be comprehended at a time.
  18. DESCARTES' EVER-VALUED CONTRIBUTIONS TO PURE MATHEMATICS Father of modern coordinate geometry. present standard textbooks consists theories from his greatest work Geometry (1637). Foundation of analytic geometry by introducing a constant-variable notion to geometry with which it is possible to express curve properties by algebraic of geometry to algebra and vice versa. algebraic treatment to solve complicated geometrical problems and geometric representation of algebraic results (eg. the value of graphs).
  19. Descartes' Rule of Signs : The rule states that if the nonzero terms of a single- variable polynomial f(x) with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign changes between consecutive (nonzero) coefficients, or is less than it by an even number. For negative roots consider sign changes in f(-x).
  20. Conic Sections First systematic classification of geometric curves into three classes according as their equation contains ; no term of higher degree than the multiple of 2 unknown quantities or the square of one (eg. Circle, ellipse, parabola, hyperbola). Ci rcle Parabola Ellipse Hyperbola
  21. one or more terms of the 3rd or 4th degree in either or both of its unknowns. a term of the 5th or 6th degree in either or both of its unknowns. The geometry led to the concept of continuity development of function theory theory of limits. discovered isomorphism between curves in a plane and equations in two variables.
  22. General rule for resolving an equation by expressing it in zero form and factorize L.H.S. or reduce it in two or more equation of lower degree. He proposed, solution for 3rd or 4th degree equation through the intersection of a circle with a conic. solution for still higher degree through intersection of circles with several classes of geometric curves, but assumptions to solve equations of any order through this point in a plane and in space using coordinates.
  23. Representing curve by a second degree equation i.e. a conic. Investigating properties of a curve by means of an equation between coordinates of any point on the curve into the language of analytic geometry. He also worked on the theory of tangents to curves and general rule for drawing tangents and normals to curves symmetric about an axis.
  24. CONTRIBUTIONS TO PHYSICS Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction (also known Descartes' law) that the angular radius of a rainbow is 42 degrees (i.e. the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 420). By reflection and refraction of light rays in water drops he explained rainbow formation.
  25. A-le also independent discovered the law of reflection using trigonometric functions. Formed modern mathematical physics along the time of Galileo and Newton. >These are the main contributions of Descartes in Optics. discovered an early form of the of conservation of momentum. He outlined his views on the universe in his Principles of Philosophy. He has also contributed in other branches of science such as Mechanics, Geology, Meteorology, Biology etc.

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