Utilização de métodos numéricos para aproximar π

Abstract

The number pi, one of the best known in mathematics, represents the relationship between the circumference of a circle and its diameter. The calculation of their decimal places is a theme already consecrated in science, however, this subject still catches the attention of the researchers. The interest is in using different computational methods and different programming languages. In this sense, the objective of this work is to obtain approximations for the number pi, using methods for approximation of real roots of equations implemented in the programming language R. The methods of bissection, false position, linear iteration, Newton-Raphson, Steffensen, Halley and Mu¨ller. To obtain approximations with a greater number of decimal places the package Rmpr was used. The results indicated that, because it is possible to obtain approximations with a reduced number of iterations, Newton’s method is presented as a great alternative to obtain approximations of pi with a high number of decimal places.