Critério para a construtibilidade de polígonos regulares por régua e compasso e números construtíveis

Abstract

This work discusses basic geometric constructions and constructions of regular polygons with ruler and compass made respecting the rules or elementary operations used by the ancient Greeks. Such constructions are initially treated in a purely geometric form and, in order to find a criterion that can determine the possibility of constructing of regular polygons, will be discussed by an algebraic bias. This algebraic treatment will show a relationship between geometry and algebra, in particular, the relationship between the vertices of a regular polygon and the roots of polynomials of a variable with rational coefficients. This algebraic treatment leads us naturally to the concept of constructability of numbers and points in a field, which will require the use of algebraic field extensions, and the criteria for the constructability of these leads to a criterion for constructability of polygons