AROUND CANTOR’S PROOF ABOUT TRANSCENDET NUMBERS EXISTENCE: a possible classroom activity

Abstract

This article, which activities are based on the text Vorträge Ūber Ausgewählte Fragen Der Elementargeometrie Ausgearbeitet Von F. Tärget, 1895, by Félix Klein, is a summary resulting from discussions with middle and upper school mathematics teachers who are Mathematics Master’s students on a National Network Graduation Program for School Teachers in Brazil, at Colégio Pedro II, Rio de Janeiro. During Topics in the History of Mathematics classes, teachers were formally introduced to the definition of transcendent irrational numbers, the demonstration of the existence of such numbers and the study of the irrationality of π, proposed by Cantor. Furthermore, they had the opportunity to prove the transcendence of an irrational number which is different from Liouville’s, but quite like some examples from High School textbooks. After that, the students were able to understand a little bit more about the evolution of mathematical thinking on the proposed topic and they could create activities that could be presented in between Brazilian High School Mathematics teachers.