Resolução de problemas da geometria euclidiana plana usando polinômios

Abstract

The main objective of this work is to solve problems and demonstrate theorems of euclidean plane geometry using polynomials. This will be done through the study of polynomial rings, polynomial systems and affins algebraic sets. These concepts makes it possible to link Algebra to Geometry. Thus, for example, by introducing cartesian coordinates into the euclidean plane, the hypotheses and conclusions of a large class of geometric theorems can be expressed with polynomial equations. We will also make use of an important computational tool, the computational algebra system Singular.