Descartes Essay, Research Paper

Descartes, Ren

Ren Descartes was born on March 31, 1596 and died on February 11, 1650. Ren Descartes was a man of many things. He was a French mathematician, philosopher and scientist. He made contributions to the theory of equations and his rule of signs, but the most distinguished contribution that Descartes made to the world of mathematics was analytic geometry.

Descartes contributed the La G om trie to analytic geometry in 1637. This was fated to become one of the most significant books in the history of mathematics. Analytic geometry is the application of algebra to geometry. In this book it shows that Descartes was the first one to use the end of the alphabet such as x, y, and z for variables. He also use the beginning of the alphabet a, b, and c for parameters. Descartes goal was to accomplish construction solutions to geometric predicaments by process of instruments that were customary to the majority of mathematicians, such as, the ruler and compass. He described instruments more general than the compass for drawing geometric curves. He specified that the parts of the instrument be coupled together so that the ratio of the motions of the parts could be foreseeable. Descartes says that the ratios between straight and curved lines are not known, and I even believe cannot be discovered by men, and therefore no conclusion based upon such ratios can be accepted as rigorous and exact.

Another contribution that Descartes mad was his rule of signs to the theory of equations. The rule of signs was a tool to help determine what type of roots, positive, negative, or imaginary, a polynomial equation has. The theory of equations were concerned with the nature of the roots of polynomial equations and with the methods of finding the roots and related problems. In Descartes rule of signs he says that the maximum number of positive roots of f(x) = 0, where f is a polynomial, is the number of changes in sign of the coefficients and that the maximum number of negative roots is the number of sign changes in f(-x) = 0.