Geometria e números construtíveis: história e prática

Abstract

This work has as main objective the search for the valuation of basic and fundamental practices such as the use of ruler and compass in the classroom. Something so neglected in several of our schools almost being abolished from various school curricula. The use of the ruler and compass in the classroom is nothing more than the most concrete and visual form of the student to see how one can construct complex geometric shapes and construct segments of lines with due measures from a previously fixed segment as unit . The demonstrations of the constructions is also of extreme relevance for the deepening of the content. Then it is welcome that the student knows some ground plane geometry as similarity of triangles, Pythagorean theorem, point power, Tales theorem, etc. The work itself does not exclude the use of GeoGebra's powerful software. In fact, the joining of the ruler and compass with GeoGebra would be ideal in the classroom. The work is divided into three parts: The first part are basic constructions such as performing angular transfer, summing the subtraction of angles, tracing the bisector of a given angle and constructing the perpendicular bisector of a given segment among others. The second part is the inscription of regular polygons given a circumference given with due justifications. The third part is the construction of rational numbers.