Uma construção da geometria analítica a partir dos teoremas de Tales e de Pitágoras.

Abstract

This work consists of a brief biographies of Thales, Pythagoras and René Descartes, as well as their contributions to the study and advancement of geometry. It comprises the proofs of the main formulas of Analytic Geometry such as: Ratio of Two Segments, Calculation of Midpoint, Distance Between Two Points, Three Point Alignment Condition, Linear Equation: Slope-Intercept Form, Linear Equation: Intercept Form, Distance from a Point to a Line, among others; showing that they are based on the Thales’s Theorem or on the Pythagorean Theorem, instigating, this way, a reflection on Analytic Geometry being related to the enunciated Theorems. At the end of the work, report an experience in the classroom, a class of 3rd year of high school, where the formulas of Analytic Geometry are presented to students, linking them with the Thales’s Theorem or Pythagorean Theorem, aiming, this way, to overcome the rejection of mathematics, particularly this content, for much of the students. Finally, we conclude that the basis of Analytical Geometry is related to the cited Theorems, because it is possible to demonstrate the formulas of analytical geometry from them.