Abstract
Simplicity is one of the attributes that enhances mathematical argumentation, but sometimes our weak mathematical culture does not allow us to appreciate that a mathematical issue with a simple appearance hides many alternatives no less attractive than the original topic. Our interest is to share experiences in the use of the history of Mathematics as a didactic tool for the elevation of mathematical culture. We illustrate our ideas with the treatment of some arithmetic properties related to irrational algebraic integers. Through these seemingly simple contents, but with various alternatives and generalizations, we also want to show that the transformations of mathematical practice have influenced argumentation practices. Keywords: mathematical argumentation, use of the History of Mathematics, algebraic integers, metallic means, Pisot-Vijayaraghavan numbers.