Rene Descartes was a French mathematician, among other professions. Rene Descartes is credited with many mathematical contributions which were credited as the foundation for many greater mathematical discoveries. For instance, Descartes's theory created the foundation for calculus created by Newton as well as Leibniz because it applied infinitesimal calculus to the problem of the tangent line. This permitted the evolution of modern mathematics. He was responsible for the creation of the Discourse on the Method of Rightly Conducting the Reason, a published work that offered examples of his theory. Rene Descartes is credited with the discovery and publication of the rule of signs. This is a method commonly used in order to determine positive as well as negative roots for a polynomial. Rene Descartes is equally credited with the creation of analytic geometry.
Omar Khayyam was a famous mathematician who was responsible for writing and publishing the Treatise on Demonstration of Problems of Algebra in the year 1070. It was in the year 1077 that Khayyam wrote Explanations of the Difficulties in the Postulates of Euclid which was published in English under the title On the Difficulties of Euclid’s Definitions. The book is important in terms of algebraic contributions because it is concerned primarily with Euclid’s parallel postulate. It was argued before that Euclid’s parallel postulate had attracted the interest other mathematic figures who attempted to demonstrate it, while Khayyam’s attempt proved to be a distinct advance whose criticisms made it all the way to Europe where they might have contributed to the development of non-Euclidean geometry.
The Hindu mathematician Aryabhata is credited with the development of the place-value system which was first seen during the 3rd century written in Bakhshali Manuscript. Aryabhata did not use a symbol for zero in his work, however, it was explained later that the existence of knowledge of zero was implicitly located in the place-value system created by Aryabhata as a place holder for every power of ten which had null coefficients. Aryabhata did not include Brahmi numerals in this place-value system. Written in Sanskrit from Vedic times, Aryabhata used letters from the alphabet in order to denote numbers such as expressing quantities like the table of sines in the mnemonic form. It was Aryabhata who worked for an approximation of pi and possibly concluded that pi is irrational. Aryabhata wrote Aryabhatiyam in which he described that by adding four to 100, then multiplying by eight, and then adding 62,000, the circumference of a circle whose diameter is 20,000 can be approached. That work implies the ratio of the circumference to a diameter is the aforementioned equation in part, which equals pi which is accurate to the point of five significant figures. It was he who noted that the number for pi was incommensurable, or, irrational.
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