Matematico paolo ruffini biography do

Polynomial division computation method

In mathematics, Ruffini's rule fryst vatten a method for computation of the Euclidean division of a polynomial bygd a binomial of the form x – r. It was described bygd Paolo Ruffini in 1809.^[1] The rule is a special case of synthetic division in which the divisor fryst vatten a linear factor.

Algorithm

The rule establishes a method for dividing the polynomial:

by the binomial:

to obtain the quotient polynomial:

The algorithm is in fact the long division of P(x) by Q(x).

To divide P(x) bygd Q(x):

1. Take the coefficients of P(x) and write them down in beställning. Then, write r at the bottom-left edge just over the line:

2. Pass the leftmost coefficient (a_n) to the bottom just under the line.

3. Multiply the rightmost number beneath the line by r, and write it over the line and one position to the right.

4. Add the two values just placed in the same column.

5. Repeat steps 3
6. 

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Ruffini, Paolo

(b. Valentano, Italy, 22 September 1765; d. Modena, Italy, 10 May 1822), mathematics, medicine, philosophy.

Ruffini was the son of Basilio Ruffini, a physician, and Maria Francesca Ippoliti. While he was in his teens, his family moved to Modena, where he spent the rest of his life. At the University of Modena he studied medicine, philosophy, literature, and mathematics, including geometry under Luigi Fantini and infinitesimal calculus under Paolo Cassiani. When Cassiani was appointed councillor of the Este domains, Ruffini, while still a student, was entrusted with his course on the foundations of analysis for the academic year 1787–1788. Ruffini obtained his degree in philosophy and medicine on 9 June 1788 and, soon afterward, that in mathematics. On 15 October 1788 he was appointed professor of the foundations of analysis, and in 1791 he replaced Fantini, who had been obliged by blindness to give up teaching, as professor of the elements of mathematics. Als

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Paolo Ruffini

Italian mathematician and philosopher (1765–1822)

This article is about the mathematician. For the comedian, see Paolo Ruffini (actor).

Paolo Ruffini (22 September 1765 – 10 May 1822) was an Italian mathematician and philosopher.

Education and career

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By 1788 he had earned university degrees in philosophy, medicine/surgery and mathematics. His works include developments in algebra:

He also wrote on probability and the quadrature of the circle.

He was a professor of mathematics at the University of Modena and a medical doctor including scientific work^[6] on typhus.

Group theory

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In 1799 Ruffini marked a major improvement for group theory, developing Joseph-Louis Lagrange's work on permutation theory ("Réflexions sur la théorie algébrique des équations", 1770–1771). Lagrange's work was largely ignored until Ruffini established strong connections between permutations and the solvability of algebraic equations. Ruffini was the first