Geometry and Consumable Numbers: History and Practice
Constructive geometry; Constructible numbers; Ruler and compass.
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 way the visual of the student to see how one can construct complex geometric shapes and construct segments of straight 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. So it is welcome that the student knows some fundamentals of flat geometry as similarity of triangles, Pythagoras theorem, point power, Tales theorem, etc ... The work itself also does not exclude the use of the powerful program of GeoGebra. 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 constructs how to construct 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 and some irrational ones. Finally, a fundamental resumption for the improvement and amplitude of the visualization of algebraic and mainly geometric concepts.