Uma proposta de abordagem ao problema de Flávio Josefo aplicada ao ensino médio

Abstract

In this paper, we presents a didactic sequence of activities designed for a group of students of high school, their age were about 15 and 18 years old, with the main objective to study the problem proposed by the mathematician Flávio Josefo, in mid-year 64. The legend tells that a group of rebels, including Flávio Josefo, was trapped in a cave by the enemy army. Preferring the suicide to capture, the rebels decided to form a circle and, counting over this, to kill each third person of the rest of the group. Josefo was contrary of this suicide pact therefore, together with a friend, calculated very quickly the appropriated positions that both should take in this circle in order to get out of this terrible situation. To understand this solution, we propose, at the first moment, a review about the numerical sequences, including the special cases of arithmetic and geometric. Then, we introduce some notions about the de recurrence relations and the Principle of Mathematical Induction, allowing a generalization of concepts and results already known intuitively by the student group.