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René Descartes (1596-1650) was a French philosopher, scientist, and mathematician. He is considered a founder of modern philosophy and the father of modern mathematics. Some of his key contributions included systematizing analytic geometry by inventing the Cartesian coordinate system, which connects algebra and geometry. He also developed the theory of equations and exponential notation. Descartes made important advances in analytic geometry that helped lay the foundations for calculus.
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Renè descartes
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- In mathematics, Descartes invented the Cartesian coordinate system, which connected algebra and geometry and paved the way for calculus. He also developed the Cartesian rule of signs for determining the nature of solutions to polynomial equations.
- As a philosopher, Descartes' most influential works were Discourse on the Method and Meditations on First Philosophy. His famous saying "I think, therefore I am" established the basis of rationalism in philosophy.
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- The development of modern scientific notation and concepts like calculus, logarithms, and probability by figures like Descartes, Newton, Leibniz, Napier, and Pascal.
- Advancements in fields like astronomy, physics, and mathematics through inventions like the telescope and discoveries in mechanics, projective geometry, and analytic geometry.
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Renè descartes
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- In mathematics, Descartes invented the Cartesian coordinate system, which connected algebra and geometry and paved the way for calculus. He also developed the Cartesian rule of signs for determining the nature of solutions to polynomial equations.
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René Descartes was a French philosopher, mathematician, and scientist born in 1596. He is known as the "father of modern western philosophy" and developed analytical geometry, bridging algebra and geometry. Descartes doubted all knowledge that was uncertain and developed his famous saying "I think, therefore I am" to establish certainty. He created a systematic method of doubt and reasoning to develop knowledge, establishing rationalism as a means to derive truth through reasoning alone rather than experience. His works had significant influence on the development of modern mathematics, philosophy, and science.
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Isaac Newton was an influential English scientist who made seminal contributions to physics, mathematics, and optics in the 17th century. Some of his major accomplishments included formulating the laws of motion and universal gravitation, which helped usher in the Classical Mechanics era. He also developed calculus and made discoveries in optics such as color theory. Newton published his work Philosophiæ Naturalis Principia Mathematica in 1687, which synthesized previous scientific ideas and laid the foundations for mechanics. Overall, Newton is widely considered one of the most influential scientists in history.
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rene_descartes.ppt
- 2. 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
- 3. 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
- 4. 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
- 5. 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.
- 6. •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 x2 to indicate squaring.
- 7. 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
- 8. The Cartesian Coordinate System Descartes developed the coordinate plane system which is widely used today
- 9. 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.
- 10. 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)