O problema da quadratura do círculo: uma abordagem histórica sob a perspectiva atual

Abstract

This work bears the purpose of setting up the course of the circle quadrature solution attempts, as well as to mention its influences, contributions for the mathematics development until now and to incentive the geometry dynamics use. In it we produce a possible explanation of how geometry has been created besides of a brief study on the number followed of the production GeoGebra software, the too we have utilized to build up the figures and the work implementations. We will utilize the areas equivalence based on Euclides elements to solve an initial problem: that of constructing a quadrilateral equivalent to a given pentagon and, for such, it will be necessary the demonstration of some propositions. We will utilize the square to relate its areas with those of the polygonal figures through the âquadratureâ method. With such we will execute the rectangle, triangle, pentagon quadrature, and that of the convex n sides polygon. We will utilize Pitagoras theorem to sum up the squares areas by bringing up brief comments about its use. Afterward this method will also the utilized in the attempt of squaring the curvelin figures such as the circle which has later on originated the problem of the circle quadrature. For explain such a problem we will utilize the geometric construction along with the demonstration of two methods for obtaining the circle quadrature and its respective results and comparisons. In the sequence, we will know what the are constructive numbers, algebraic and transcendent, which will enable us to reach to a classification of the number and its relation to the circle quadrature problem, reaching out the answer to our problem. While defining the geometrical average we will demonstrate how to obtain some quadrature utilized in such an average in the proposed activities. In other words, we can say that this work aims to produce the circle quadrature problem, the investigation of the methods developed by mathematicians for the solution of this problem in the course of history and, finally, an ascertainment on the answer these methods point us.