Why ?2 is irrational? Seeking explanations in the processes of thought experimentation

Abstract

This article is one of the results of the theoretical research entitled The Thought Experiments as Alternative Methodology for the teaching of Mathematics. The intention of this text is to present an epistemological discussion about the idea of irrational numbers, highlighting  In this context, we present the Thought Experiments as a possible alternative methodology for the teaching of Mathematics, helping the debate and raising contradictions and possibilities in the exploration of the theme. These experiments are ways of exposing thoughts by means of representations, as an object of consideration in a given mathematical activity and/or proof, using a well-defined theoretical context. Such experiments are only possible to be applied to the teaching of this science, if we consider that Mathematics is a semiotic activity that builds diagrams, experiments in these diagrams, and verifies the possible results.